var textForPages = ["9 788021 075573                                                   2 0 14                                                                                   ISBN 978-80-210-7557-3                                                                                   DOI: 10.5817/CZ.MUNI.M210-7557-2014                                      Administration, Masaryk University                                                                                                  PUDIL,  BLAŽEK   et al.                                           Faculty of Economics and                                                      \&                                       University of Economics, Prague                                            Faculty of Management                                                                                                  2014                                                                                                  Identifying Corporate Performance Factors Based on Feature Selection                                                                                                                                                                                                               Faculty of Management                                                                                                                                                                                                    University of Economics, Prague                                                                                                  Identifying Corporate Performance Factors Based on Feature Selection                                                                                                                                                                                                                                             \&                                                                                                                                                                                                             Faculty of Economics and                                                                                                                                          Faculty of Management                                                                                                                                                                                               Administration, Masaryk University                                                                                                                                     University of Economics, Prague                                                                                                                                                   \&                                                                                                                                         Faculty of Economics and                                                                                                                                    Administration, Masaryk University  Identifying Corporate Performance                                                                                                                                                               Factors Based on Feature Selection in                                                                                                                                                                              Statistical Pattern Recognition                                                                                                                           Identifying Corporate Performance                   M E T H O D S ,   A P P L I C AT I O N ,   I N T E R P R E TAT I O N                                                                                                                          Factors Based on Feature Selection in                                      Pavel Pudil, Ladislav Blažek,                                                                                                                              Statistical Pattern Recognition                    Ondřej Částek, Petr Somol, Jana Pokorná,                                                                                                                                                                                                                          Maria Králová                                                                                                                              METHODS, APPLICATION, INTERPRETATION                                                                                                                                      Pavel Pudil, Ladislav Blažek,                                                                                                                               Ondřej Částek, Petr Somol, Jana Pokorná,                                                                                                                                            Maria Králová                                                                           2014                                                                                                                                                     2014                                                                                                          2014                                              Faculty of Management t                              Faculty of Managemen                          University of E University of Economics, Pragueconomics, Prague                                        \&             \&                             Faculty of Economics and                                           Faculty of Economics and                                                                                                  PUDIL,  BLAŽEK   et al.                                      Administration, Masaryk Universityasaryk University                        Administration, M                                                                                      DOI: 10.5817/CZ.MUNI.M210-7557-2014                                                                    DOI: 10.5817/CZ.MUNI.M210-7557-2014                                                                     ISBN 978-80-210 ISBN 978-80-210-7557-3-7557-3                                      2 0 14       2 0 14                                                                       9 788021 07   9 788021 0755735573  PUDIL,  BLAŽEK   et al.  2014  Identifying Corporate Performance Factors Based on Feature Selection  Factors Based on Feature Selection in                                                                                     9 788021 0755735573                                                                     9 788021 07                                                    2 0 14                                      2 0 14                                                                                   ISBN 978-80-210-7557-3-7557-3                                                                     ISBN 978-80-210                                                                     DOI: 10.5817/CZ.MUNI.M210-7557-2014                                                                                   DOI: 10.5817/CZ.MUNI.M210-7557-2014                                          Administration, Masaryk Universityasaryk University                        Administration, M                                           Faculty of Economics and                             Faculty of Economics and                                                      \&                                        \&                          University of E                                       University of Economics, Pragueconomics, Prague                                            Faculty of Management t                              Faculty of Managemen                                                                                                                                                           2014                                                                                                                                                 Maria Králová                                                                                                                               Ondřej Částek, Petr Somol, Jana Pokorná,                                                                                                                                     Pavel Pudil, Ladislav Blažek,                                                                                                                               METHODS, APPLICATION, INTERPRETATION                                                                                                                                Statistical Pattern Recognition                                                                                                                              Identifying Corporate Performance                                                                                                                                        Administration, Masaryk University                                                                                                                                         Faculty of Economics and                                                                                                                                                   \&                                                                                                                                     University of Economics, Prague                                                                                                                                          Faculty of Management","","Castek_1_Castek - kopie  23.1.2015  7:35  Stránka 1                                        Identifying Corporate Performance Factors Based                   on Feature Selection in Statistical Pattern Recognition                    METHODS, APPLICATION, INTERPRETATION","Castek_1_Castek - kopie  23.1.2015  7:35  Stránka 2                    2","Castek_1_Castek - kopie  23.1.2015  7:35  Stránka 3                                                                                                   3                                Identifying Corporate Performance Factors Based                   on Feature Selection in Statistical Pattern Recognition                    METHODS, APPLICATION, INTERPRETATION                         Pavel Pudil, Ladislav Blažek, Ondřej Částek,                   Petr Somol, Jana Pokorná, Maria Králová                                                     FACULTY OF ECONOMICS AND ADMINISTRATION                   MASARYK UNIVERSITY                   BRNO                   2014","Castek_1_Castek - kopie  23.1.2015  7:35  Stránka 4                                        Team of authors:                   prof. Ing. Pavel Pudil, DrSc. (3, 4)                   prof. Ing. Ladislav Blažek, CSc. (1, 6)                   Ing. Ondřej Částek, Ph.D. (1, 2, 5)                   RNDr. Petr Somol, Ph.D. (3, 4)                   Ing. Jana Pokorná (2)                   Mgr. Maria Králová, Ph.D. (5)                    Translation by Mgr. et Mgr. Bc. Milan Boháček, M.A.                   Corrections by Steven Del Riley, BA                   Cover designed by Petr Somol                    Reviewers:                   prof. Ing. Michal Haindl, DrSc.                   doc. Ing. Robert Zich, Ph.D.                    This work has been supported by the Grant Agency of the Czech Republic – project                   No. P403/12/1557                                   BY                   CC BY 4.0 Crea�ve Commons A�ribu�on 4.0                     © 2014 Masarykova univerzita                   © 2014 Pavel Pudil, Ladislav Blažek, Ondřej Částek, Petr Somol, Jana Pokorná,                          Maria Králová                    ISBN 978-80-210-7557-3                   ISBN 978-80-210-7672-3 (online : pdf)                   DOI: 10.5817/CZ.MUNI.M210-7557-2014","Castek_1_Castek - kopie  23.1.2015  7:35  Stránka 5                                                                                                   5                               Contents                            Introduction                                                             9                    1 Formulation of objectives and methodological approach                11                     1.1 Summary of previous research activities                          11                     1.2 Methodology of current research                                  16                    2 Competitiveness and its measurement                                  21                     2.1 The term competitiveness                                         21                     2.2 Approaches to measuring competitiveness                          22                         Financial performance                                            23                     2.3 Financial performance indicators used                            24                     2.4 Period of performance measurement                                25                     2.5 The development of performance measurement methodology           26                         2.5.1 Cluster analysis                                           27                         2.5.2 Hyperbola                                                  28                         2.5.3 Summation                                                  30                         2.5.4 Quintiles                                                   31                     2.6 Assessing the appropriateness of methods to measure financial    32                         performance                                                      33                         2.6.1 Experiment settings                                        33                         2.6.2 Experiment output                                          36                     2.7 Description of the methodology used to measure performance       39                   3 Feature Selection Methods in Statistical Pattern                     Recognition                                                          39                     3.1 Introduction                                                     40                         3.1.1 Common Research Issues in Machine Learning and Management  41","Castek_1_Castek - kopie  23.1.2015  7:35  Stránka 6                    6  CONTENTS                       3.2 Dimensionality Reduction                                         41                         DR Categorization According to Nature of the Resulting Features  42                         DR Categorization According to the Aim                           42                     3.3 Feature Subset Selection                                         44                         3.3.1 FS Categorization With Respect to Optimality               44                         3.3.2 FS Categorization With Respect to Selection Criteria       45                         3.3.3 FS Categorization With Respect to Problem Knowledge        46                     3.4 Sub-optimal Search Methods                                       47                         3.4.1 Best Individual Features                                   48                         3.4.2 Sequential Search Methods and their Evolution              48                              Floating search methods                                     50                              Oscillating search method                                   50                         3.4.3 Non-sequential and alternative methods                     52                         3.4.4 Pitfalls of feature subset evaluation – experimental comparison                              of criterion functions                                      53                         3.4.5 Summary of recent sub-optimal feature selection methods    54                         3.4.6 Dependency-Aware Feature Selection (DAF)                   55                     3.5 Performance Estimation Problem                                   58                     3.6 Problem of Feature Selection Overfitting and Stability           59                         3.6.1 Problem of Feature  Selection Stability                    61                     3.7 Summary                                                          61                    4 Testing approaches and methods based                     on learning methods for identifying factors                     of competitiveness                                                   63                      4.1 Introduction                                                     63                     4.2 Feature selection based evaluation of competitiveness factors    67                         4.2.1 Feature Selection Methodology                              68                         4.2.2 Evaluating Stability of Feature Selection Methods          69                     4.3 Introducing the modified feature selection methodology           71                         Non-Parametric Model                                             71                         Handling Missing Values and Non-Numeric Values                   71                     4.4 Pattern classification approach                                  72                     4.5 Regression approach and pseudo-kernel regression model           72                     4.6 Experiments and results                                          75                         4.6.1 Regression-based analysis results                          75                         4.6.2 Classification-based analysis results                      78","Castek_1_Castek - kopie  23.1.2015  7:35  Stránka 7                                                         1.1 SUMMARY OF PREVIOUS RESEARCH ACTIVITIESCONTENTS  7                       4.7 Comparing Regression-based and Classification-based analysis results  79                     4.8 Improved Model for Attribute Selection on High-Dimensional                         Economic Data                                                    80                         4.8.1 Improvements of the regression model                       80                              Varying the distance function                               80                              Kernel width multiplication constant                        83                         4.8.2 Optimized model performance on 37- and 74-dim data         85                     4.9 Conclusions                                                      88                   5 Identifying factors of competitiveness using                     bivariate analyses and linear regression analyses                    91                     5.1 General characteristics                                          92                         Effect of company size on the financial performance              92                         Effect of industry on the financial performance                  94                         Interaction of company size and industry                         94                     5.2 Internal competitiveness factors of a company                    98                         Multidimensional model                                           99                     5.3 External competitiveness factors of a company                   100                         Multidimensional model                                          102                     5.4 Stakeholder orientation and characteristics of an organizational                         structure                                                       103                         Multidimensional model                                          106                     5.5 Owners                                                          106                         Multidimensional model                                          110                     5.6 Employees                                                       112                         Multidimensional model                                          114                     5.7 Customers                                                       116                         Multidimensional model                                          118                     5.8 Suppliers                                                       120                         Multidimensional model                                          122                     5.9 Corporate social responsibility                                 124                         Multidimensional model                                          125                     5.10 Comprehensive model                                            126                   6 Interpretation of the results achieved                              129                     6.1 Overall characteristics of the sample                           131                     6.2 Identification of typical combinations of factor values leading                         to certain types of financial performance                       143","Castek_1_Castek - kopie  23.1.2015  7:35  Stránka 8                    8  CONTENTS                           Group A as a whole                                              143                         Group A 1                                                       145                         Group A 2                                                       146                         Group A 3                                                       148                         Group A 4                                                       149                         Group A 5                                                       150                     6.3 Summary                                                         152                    7 Conclusion                                                          155                   8 Bibliography                                                        159                    List of Figures                                                       167                   List of Tables                                                        168                    List of Graphs                                                        170","Castek_1_Castek  23.1.2015  7:37  Stránka 9                                                                                                   9                                  Introduction                          The issue of finding competitiveness factors of companies represents a very topical                   and interesting subject in terms of both practice and theory, with many publications                   dealing with this issue. However, these works do not present a uniform way of                   thinking, as they vary in their approach to the issue, terminology used, applications                   of the methods, solution justifications, and even in the credibility of the results                   achieved and their interpretation. This raises such questions as (1) how to express                   corporate competitiveness, (2) how to measure the effect of potential factors of                   competitiveness in a multidimensional space under the conditions typical for business                   research, and finally, (3) what are the competitiveness factors and how can we interpret                   their effects?                       This publication presents the results of research focusing precisely on this area.                   It deals with the issue of applying selected statistical methods to identify the                   competitiveness factors of companies so as to respect the synergistic effect of their                   influence.                       The theoretical and methodological part of this monograph describes the                   approach to the way of expressing the financial performance of companies, and                   especially approaches to the identification of factors that affect the financial                   performance. Experiments with an application of these approaches are described and                   analysed using empirical data of companies from manufacturing and construction                   industries, including interpretation of the results achieved.                       The research was conducted in the period of 2012-2014 under a project of the                   Grant Agency of the Czech Republic entitled, “Developing Methods for Identifying                                                                                   1                   and Evaluating Factors That Critically Affect Corporate Performance” as a joint                   research project of the University of Economics in Prague, Faculty of Management in                   Jindřichův Hradec, and Masaryk University, Faculty of Economics and Administration                   in Brno.                      1  This work has been supported by the Grant Agency of the Czech Republic – project No. P403/12/1557.","Castek_1_Castek  23.1.2015  7:37  Stránka 10                   10","Castek_1_Castek  23.1.2015  7:37  Stránka 11                                                                                                   11                               1 Formulation of objectives and methodological                       approach                          The presented work deals with analysing and formulating methodology on the search                   for competitiveness factors of companies, including its verification and interpretation                   on an extensive sample of empirical data.                       This work builds on several years of research in the given field, conducted by the                   research team of the Centre for the Competitiveness of the Czech Economy established                   at the Faculty of Economics and Administration at Masaryk University. The results of                   this work are summarized in the monographs by Blažek et al. (2007), Blažek et al.                   (2008) and Blažek et al. (2009). In order to better understand the focus and purpose                   of the presented work, we consider it necessary to briefly summarize these research                   activities.                      1.1 Summary of previous research activities                     The main focus of the research was on the competitiveness of companies, namely the                   search for the factors that affect it. In other words: finding the reasons why some                   businesses are competitive and others are not. In addition to this, it found certain                   types of businesses that were competitive, and conversely other types of businesses                   that in turn are not.                       The researchers pursued the idea that these factors can be identified on the basis                   of a sophisticated analysis of empirical data and that it is also possible to identify                   typical configurations of values of these factors which impact the level of                   competitiveness that individual businesses achieve. In other words: the same or similar                   level of competitiveness can be achieved in different ways. Two companies reaching                   the same level of competitiveness may differ from each other very significantly.                       When elaborating this issue, it was of course necessary to proceed to the                   operationalization of the key concepts. This concerned mainly the concept of                   “competitiveness”, which proved to be too vague, elusive and difficult to measure for                   the sake of further analysis. Therefore, it was replaced with the term “economic success”.","Castek_1_Castek  23.1.2015  7:37  Stránka 12                   12  1 FORMULATION OF OBJECTIVES AND METHODOLOGICAL APPROACH                         The population was defined as follows:                       – companies based in the Czech Republic (territorial aspect),                       – companies in all industries (industry aspect),                       – companies with 50 or more employees (size aspect),                       – joint-stock companies and private limited companies (aspect of a legal form).                       The empirical survey was conducted in two stages. The subject of the first one                   included those industries that represent key areas of the business sector of the Czech                   economy, i.e. the manufacturing and construction industries. In the second stage,                   other sectors were analysed. Since the number of companies that fit the definition                   above is too low for a statistical analysis in some of these industries, the size limit was                   reduced to 10 workers in the second stage.                       Population specified this way included about 8,000 companies at the time of the                   survey.                       There were two primary sources of information for solving the task in question:                       – data from the questionnaires, capturing the selected characteristics of                          companies,                       – data from public databases (Albertina Data), capturing the selected financial                          indicators.                       Those companies that were in bankruptcy or liquidation at the time of the survey,                   as well as those businesses whose data were missing in the database, were excluded                   from the population.                       The population that was subsequently used included 4,915 companies. This set                   was considered the population for the purpose of the research.                       However, it was obviously impossible to subject such a large set to a questionnaire                   survey. There were two main reasons:                       – the over-whelming effort,                       – the unwillingness of most businesses to participate in the questionnaire survey.                       Companies from the population were asked to participate in the questionnaire                   survey in such a way that self-selection determined by the willingness or unwillingness                   of the surveyed companies could be restricted or eliminated by a quota selection. In                   accordance with the definition of the population, the quota variables included territory                   (regions), industry, size, and legal form of business. The percentage representation in                   the population and the sample showed very close values on average. This indicates                   that the sample can be considered representative. The questionnaire survey was                   conducted in collaboration with Augur Consulting.                       The methodology of the task in question is shown in Figure 1-1.                       1. Questionnaire data                       As previously mentioned, the questionnaire survey was conducted in two stages.                   In the first sub-stage (2007), which applied to companies from the manufacturing and                   construction industries, 432 companies participated in the empirical survey. In the                   second sub-stage (2009), which applied to companies from other industries, the survey                   included 267 companies.","Castek_1_Castek  23.1.2015  7:37  Stránka 13                                                         1.1 SUMMARY OF PREVIOUS RESEARCH ACTIVITIES  13                     Figure 1-1: The methodology of previous research activities                              1. Ques onnaire data                       2. Accoun ng data                                3. Primary analysis               4. Clustering based on economic success                              5. Secondary analysis                                          6. Iden fica on of factors of economic success                                         7. Clustering based on factors of economic success                                                 8. Economic interpreta on                           2. Accounting data                       In the case of the first sub-stage, data from the financial statements for the years                   2002 to 2006 were used; in the second sub-stage, data from the financial statements                   for the years 2002 to 2007 were used.                        3. Primary analysis                       The primary analysis involved evaluating frequencies of responses to the                   questions of the questionnaire; the questionnaires produced almost 700 variables. The                   results were presented in the form of tables and graphs, including comments briefly                   interpreting the presented numerical and graphical information. The evaluation was                   performed for the sample as a whole as well as for the sub-samples, categorized by                   industry, company size, and legal form of business. A number of important pieces of                   information concerning the businesses were obtained in this way (Blažek et al., 2007,                   p. 41–287; Blažek et al., 2009, p. 29–262). However, the main output of the primary                   analysis was the processing of the variable set, entering the secondary analysis.                        4. Clustering based on economic success                       Economic success was evaluated on the basis of two indicators, i.e. return on                   assets and asset growth indicators. In the first sub-stage, the sample of 432 companies","Castek_1_Castek  23.1.2015  7:37  Stránka 14                   14  1 FORMULATION OF OBJECTIVES AND METHODOLOGICAL APPROACH                     was structured based on the application of a cluster analysis into three groups (A, B                   and C), from the most efficient to the least efficient (Blažek et al 2008, p. 53–66). In                   the second sub-stage, this methodology was largely modified. The sample of 267                   companies was also structured into three groups (A, B and C); however, in this case                   the basis was not a cluster analysis but the so-called “coefficient of economic success”                   (Blažek et al., 2009, p. 53–66).                        5. Secondary analysis                       The purpose of this analysis was to transform the set of variables from the primary                   analysis into a set of variables as potential factors of economic success, suitable as an                   input into the methods of multidimensional statistical pattern recognition. Using the                   application of common statistical methods, the relationship between different                   variables and economic success of companies was analysed. There was a significant                   reduction in the number of variables; variables with a low variation and variables with                   a high proportion of missing values were excluded. In many cases, it was necessary to                   do a recoding into new variables, suitable for the subsequent mathematical and                   statistical procedures and interpretation of the obtained results (Blažek et al., 2008, p.                   31–39 and p. 67–88, Blažek et al., 2009, p. 275–277).                        6. Identification of factors of economic success                       In order to ensure the exact mastering of this statistically demanding task, selected                   methods of statistical pattern recognition were used for the multidimensional analysis.                   Specifically, these methods included Individual Best Search (IBS), Sequential Floating                   Search (SFS) and Sequential Floating Forward Search (SFFS). The outcome of the                   application was to identify which variables tested by these methods are the factors                   that influence decisively the economic success of the companies analysed; moreover,                   the outcome did not seek to identify the factors that influence the economic activity                   separately, i.e. each factor individually, but integrally, i.e. interrelated (Blažek et al.,                   2008, p. 89–93, Blažek et al., p. 275–280).                        7. Clustering based on factors of economic success                       After identifying the factors of economic success, it was necessary to find such                   typical configurations of values of these factors that are produced by certain types of                   economic success achieved by companies. Clusters based on factors of economic                   success were created using the application of the cluster analysis method within each                   of the groups A, B and C, created on the basis of the economic success of the                   businesses. (Blažek et al., 2008, p. 93 and 94).                        8. Economic interpretation                       Groups of companies, established on the basis of such clustering, were                   characterized with values of economic-success factors, and supplemented with several                   other variables with regard to increasing the rate of illustrativeness. First, the","Castek_1_Castek  23.1.2015  7:37  Stránka 15                                                         1.1 SUMMARY OF PREVIOUS RESEARCH ACTIVITIES  15                     interpretation of characteristic features at the level of the entire sample was made,                   using the comparison of factor values and selected variables between the groups of                   companies A, B, and C, grouped according to their economic success. Subsequently,                   a similar interpretation was conducted at a more detailed level – within the group of                   the economically most successful companies (group A); it included the comparison                   of values of the same factors and variables as in the previous case, but between groups                   of companies created by secondary clustering, i.e. by factors of economic success                   (Blažek et al., 2008, p. 95–120).                       After some time it can be stated that the research described above represents a                   challenging and somewhat unique event, both in terms of the methodological                   approach and the extent of empirical investigation. Despite the obvious benefits,                   however, many of the problems that occurred during the solution and the complexity                   of some of the results achieved remained unresolved.                       This primarily concerns the methodological level. When searching for the best                   way to apply approaches based on pattern recognition when identifying the factors                   of economic success, a number of experiments were performed. Although some useful                   experience was obtained thanks to these experiments, the results obtained did not                   lead to unambiguous conclusions. The researchers failed to overcome the negative                   phenomenon of excessive sensitivity of outputs to relatively small changes in input                   variables as well as a relatively strong influence of the choice of a particular evaluation                   algorithm and its parameters on the obtained results.                       The quality of the results, both in the primary and secondary analyses and in                   identifying the factors of economic success of businesses, was also undoubtedly                   limited by the character of the industries in question. In the first stage, the                   investigation focused on manufacturing and construction industries, i.e. industries                   producing material goods, industries with relatively strong internal homogeneity,                   exclusive entrepreneurial orientation, and consequently with many companies whose                   legal form was private limited company or joint-stock company. However, in the case                   of the second stage, the situation was quite different: it was basically a conglomerate                   of nine industries, many of which showed diametric differences with respect to one                   another. The main factor that fundamentally undermined the homogeneity of the                   sample was the fact that only some of these industries can be considered                   entrepreneurial, while in others entrepreneurship is practically non-existent. This is                   closely connected with the representation of private limited companies and joint-                   stock companies. The representation of the respondents in each industry was                   therefore very uneven. Three of the nine industries analysed included fewer than 10                   respondents. The effort for the widest possible coverage unfortunately resulted in                   comparing, or evaluating jointly, industries that are difficult to compare by nature,                   or even incomparable.","Castek_1_Castek  23.1.2015  7:37  Stránka 16                   16  1 FORMULATION OF OBJECTIVES AND METHODOLOGICAL APPROACH                     1.2 Methodology of current research                     These facts became a challenge for further research, which was conducted within the                   project of the Grant Agency of the Czech Republic entitled “Approaches to                   identification of corporate performance factors with emphasis on methods of feature                   selection in statistical pattern recognition.” The outcomes of this research are presented                   in this publication.                       The objective of the research conducted within this project is formulated as                   follows:                       To develop and verify a methodology for identifying and evaluating factors which                   have a significant effect on the performance of companies.                       The solution involved these successive steps:                       a) Search of relevant literature, summary of theoretical knowledge.                          – Approaches to expressing competitiveness, financial performance                             measurement methods.                          – Methods of feature selection in statistical pattern recognition.                       b) Testing on the task in question                          – Testing methods for factor identification. Selecting the most appropriate                             method, improving and adjusting it. Factor identification.                          – Regression analysis: explaining financial performance on the basis of                             identified factors.                       c) Economic interpretation and overall evaluation                          – Identification and economic interpretation of typical combinations of                             factor values leading to certain types of financial performance.                       Step a) formulates theoretical grounds and creates a methodological background                   for the solution of the given task. It is contained in chapter 2. Competitiveness and its                   measurement, and in chapter 3. Feature Selection Methods in Statistical Pattern                   Recognition.                       Steps b) and c) concerning testing and interpretation were conducted following                   step a). These research activities and their results are contained in chapters 4. Testing                   approaches and methods based on learning methods for identifying factors of                   competitiveness, 5. Identifying factors of competitiveness using bivariate analyses and                   linear regression analyses, and 6. Interpretation of the results achieved.                       We will use the comments to Figure 1-2. as the first introduction to the solution                   of the task in question including its relation to previous research activities.                        1. Questionnaire data                       With respect to the above-mentioned facts, the research used data from the                   questionnaire survey conducted in 2007, which applied to companies from the                   manufacturing and construction industries. Within these two major industries, 432                   companies participated in the empirical survey. Businesses from other industries were                   not included.","Castek_1_Castek  23.1.2015  7:37  Stránka 17                                                              1.2 METHODOLOGY OF CURRENT RESEARCH  17                     Figure 1-2: Methodology of current research activities                              1. Ques onnaire data                       2. Accoun ng data                               3. Primary analysis            4. Clustering based on financial performance                              5. Secondary analysis                          6. Bivariate analysis and linear regression  7. Sta s cal pa ern‐recogni on                                                       8. Clustering based on factors of financial performance                                                  9. Economic interpreta on                            2. Accounting data                       The data used came from the financial statements for the years 2004 to 2010. The                   relationship between cause and effect was substantially respected in this way, where                   the cause refers to the company characteristics identified through a questionnaire                   survey, and the result is the development of a company’s financial indicators. Another                   important reason for choosing this period was the effort to capture the development                   of these indicators during the crisis when the competitiveness of companies was tested                   in very difficult conditions.                        3. Primary analysis                       The starting point was the primary analysis from the previous research. With                   regard to the application of subsequent procedures and methods, the available data                   were further modified.                         4. Clustering based on financial performance                       The term “economic success” was replaced with the term “financial performance”                   with regard to better operationalization. The indicators of return on assets and asset                   growth were used again, but the method of their calculation was changed substantially                   (see Chapter 2).","Castek_1_Castek  23.1.2015  7:37  Stránka 18                   18  1 FORMULATION OF OBJECTIVES AND METHODOLOGICAL APPROACH                         5. Secondary analysis                       Similarly to the primary analysis, the secondary analysis was also based on the                   previous research. However, the reduction of the number of variables entering the                   experiments of statistical pattern recognition did not have to be so dramatic because                   the newly applied DAF algorithm is not so sensitive to the ratio of the number of input                   variables to the number of available observations (i.e. companies). Therefore, the                   number of variables from the questionnaire was reduced on the basis of value                   variability and the number of missing values to 74 variables instead of 37 variables                   used in the SFFS algorithm.                         6. Bivariate analysis and linear regression                       Usual methods of bivariate analysis, i.e. t-tests, ANOVA and correlation and                   association analyses were used in parallel with the experiments of statistical pattern                   recognition. In addition, partial linear regression models were also formulated. These                   analyses provided a number of findings on the relationships between the                   aforementioned 74 variables and financial performance (see Chapter 5). When                   comparing the power of the relationship found by these procedures and the error of                   estimation of a nonlinear model based on the variables selected by the DAF method,                   the advantage of using the techniques of statistical pattern recognition is obvious. This                   section thus serves as a direct comparison of the results of both approaches as well as                   assistance for economic interpretation (see the final step).                        7. Statistical pattern-recognition                       Unlike in the previous research, a different approach of multidimensional analysis                   was applied in this fundamental research activity. Specifically, it was the DAF                   algorithm, which shows a much higher stability of results for the given task than the                   SFFS algorithm which was originally used. Moreover, the non-linear regression model                   was employed as a better classifier than the original k-NN classifier; the DAF                   algorithm was also improved in several aspects, which resulted in an increase in the                   accuracy of the result.                         8. Clustering based on factors of financial performance                       The procedure was similar to the previous research; however, the difference                   consisted in clustering that was conducted using different factors of financial                   performance and within different groups of companies, created based on their                   financial performance (see Chapter 6).                         9. Economic interpretation                       The researchers again proceeded similarly as in the previous research, but with                   different variables and a different grouping of companies according to their financial                   performance. This time, the companies were divided into quartiles. They were labelled                   as groups A, B, C and D, where group A included businesses with the highest financial","Castek_1_Castek  23.1.2015  7:37  Stránka 19                                                              1.2 METHODOLOGY OF CURRENT RESEARCH  19                     performance and group D businesses with the lowest financial performance. First, an                   interpretation was performed at the level of the entire selected sample, using the                   comparison of factor values and selected variables between the A, B, C and D company                   groups. Next, a similar interpretation was performed at a more detailed level – within                   the group financially most powerful companies, in order to interpret the mainly                   quantitative representation into the representation of the mainly qualitative nature                   (see Chapter 6).                    This book also summarizes and builds on some already published outputs of this                   project, particularly the following ones. In the work-in-progress paper, Pudil et al.                   (2012) compared the performance and stability of algorithms SFFS and DAF                   combined with the k-NN classifier. The result was that DAF algorithm achieves a                   slightly higher accuracy but significantly higher stability. Částek et al. (2013) proved                   the necessity of using advanced multivariate methods by comparing different                   approaches on the same data set and paper. Pokorná and Částek (2013) reviewed                   methods of corporate performance measurement and experimentally verified a chosen                   way, longitudinal combination of ROA and Growth of Assets. Pudil et al. (2013)                   finished the comparison of SFFS and DAF; this time these algorithms were combined                   with a non-linear regression instead of the k-NN classifier. Again, this approach                   improved both the accuracy and stability of the results and again the DAF algorithm                   was found higher performing in both criterions. The final step was taken in the paper                   by Somol et al. (2014). Here, the distance function and kernel width used were                   optimized and accuracy has risen once again with no loss of stability.                       The use of DAF algorithm together with multivariate regression model for                   predicting financial performance measured by adding up ROA and Growth of Assets                   became the basis for selecting the factors of corporate performance. Besides that, the                   reader will also find a procedure for interpreting such factors in this book, including                   the actual interpretation of the effect of these factors in Czech construction and                   manufacturing companies.","Castek_1_Castek  23.1.2015  7:37  Stránka 20","Castek_1_Castek  23.1.2015  7:37  Stránka 21                                                                                                   21                                  2 Competitiveness and its measurement                          The term competitiveness is widely used but not a uniformly understood one. Authors                   of various studies often create their own definitions, which imply different approaches                   to measuring competitiveness. Therefore, in this chapter we focus on the term                   competitiveness, explain the possibilities of its measurement, and finally, justify the                   choice of the methodology used to measure competitiveness in this research.                      2.1 The term competitiveness                     Competitiveness can be viewed from a macroeconomic or microeconomic                   perspective. The macroeconomic view deals with competitiveness of countries and                   their ability to produce products and services (through businesses) that are successful                   in international markets. The European Union understands competitiveness as the                   ability of an economy to increase productivity, as the only way to achieve sustainable                   growth in per capita income, which subsequently leads to the growth of living                   standards (European Commission, 2011). The World Economic Forum puts greater                   emphasis on the economy as a set of institutions and policies in understanding                   competitiveness (Schwab, 2012), through which the level of productivity of enterprises                   and thus the entire country is influenced.                       The microeconomic perspective of competitiveness, which we follow in this research,                   concerns the competitiveness of smaller units, namely businesses. The Organization for                   Economic Co-operation and Development (OECD) defines competitiveness of a business                   as its ability to compete, increase profits and growth. Approaches of other authors (Jirásek,                   2000; Blažek, 2009) can be summarized in a widely accepted definition of competitiveness                   of a business as the ability of a business to operate on the market in the long term and                   sustainably in competition with other businesses. This view of competitiveness was used                   by the Research Centre for the Competitiveness of the Czech Economy (Blažek et al.,                   2009), which this research partly follows. Factors leading to a higher ability of a business                   to stay in the market are the subject of this research.","Castek_1_Castek  23.1.2015  7:37  Stránka 22                   22  2 COMPETITIVENESS AND ITS MEASUREMENT                     2.2 Approaches to measuring competitiveness                      Higher competitiveness of a company is reflected in the long-term growth of its profits                   or increasing its market share and the consequent growth of the company as such.                   However, there is no single correct approach to measuring competitiveness, as it is                   always necessary to particularly consider the purpose and possibilities of this                   measurement. The research is therefore based on the assumption that in the long run,                   a company’s competitiveness affects the success or failure of a company in competition                   (Blažek et al., 2009). From this perspective, the success of a company can be identified                   with its performance for the purpose of its measuring. Thus, business performance is                   conditioned by its competitiveness and it should be true that if a company is                   competitive, it is also efficient (Suchánek, 2005). As a result, we transformed the                   problem of identifying factors of competitiveness of companies into the form of                   corporate performance factor identification.                       Business performance in general represents the degree of achieving the set                   objectives. Based on an organization’s objectives, we identify financial performance,                   operational performance and overall effectiveness (Hult et al., 2008).                       The widest approach is undoubtedly measuring a company’s overall effectiveness.                   This includes an analysis of achieving the long-term strategy of a company in all areas                   of its activity. However, measuring it is very problematic and often made more difficult                   by considerable subjectivity, as it includes variables such as reputation, perceived                   performance, achievement of goals, or survival. Analysing the overall effectiveness of                   a company requires extensive knowledge about the organization and its field, and it                   can be applied in qualitative research.                       Operational performance focuses on the non-financial dimension of                   performance, such as measuring the quality of products and processes in a company,                   the cycle time and productivity. The results are especially useful for business                   management in supporting the improvement of business processes or even                   benchmarking.                       The prevailing approach to performance measurement in quantitative research                   is the design of financial performance indicators (Hult et al., 2008), measuring the                   economic situation of a company. Financial analysis indicators based on accounting                   data and information from financial statements are widely used. Indicators of a                   company’s market position offer an additional view. The advantage of this approach                   is especially the easy accessibility of financial statements that are publicly accessible                   in the Register of Companies or other databases. Indicators use “hard” data from                   financial statements; therefore, they are not affected by the evaluator’s subjective view.                   Based on the purpose of the research, a historical view of a company, as well as possible                   oversimplification or disregarding industry specificities can be seen as a disadvantage.                   A possible disadvantage of long-term studies is the risk of errors arising from changes                   in the accounting procedures of the company.","Castek_1_Castek  23.1.2015  7:37  Stránka 23                                                        2.2 APPROACHES TO MEASURING COMPETITIVENESS  23 23                         The quantitative nature of this research with a large number of monitored                   companies allows us to measure performance solely from the financial perspective.                   Understanding the specific circumstances of each company would not be practically                   feasible, whereas data from the financial statements are available from databases such                   as Albertina CZ. Due to the possibility of comparing the results of this research with                   other studies and also for practical reasons, we decided to measure business                   performance using financial indicators.                     Financial performance                    The most commonly used indicators are the indicators of financial analysis, which                   can be obtained from the financial statements of a company. This includes indicators                   of profitability, frequently used by researchers, as well as indicators of debt, liquidity                   and activity. Their popularity is due to the good availability of data, simplicity of their                   design, easy interpretability and wide applicability. Ratio indicators allow us to                   compare companies of different sizes and from different industries, or to compare the                   results of a company with the recommended values. Another advantage is that the                   data for calculating these indicators are subject to internal and external checks and                   they are not influenced by “market sentiment” (Krivogorsky \& Grudnitski, 2010, p.                   182). On the other hand, they may be negatively affected by differences in accounting                   procedures (concerning the comparison between countries) or even manipulations                   such as undervaluing assets (Sanchez-Ballesta \& García-Meca, 2007).                       Another group is represented by market measures. Shareholder-value measures                   are based on the perception of a company as a tool whose purpose is to increase the                   value of the owners’ investment. These indicators are based on the value of a company’s                   shares on the market. This, however, may be affected even by external factors besides                   business performance. These indicators are not useful for quantitative research in the                   Czech Republic since there are only a few dozen listed companies on the Stock                   Exchange. The category of market measures also includes the indicators of market                   share, which, however, are not commonly accessible.                       Hybrid indicators try to capture business performance from many perspectives,                   combining multiple indicators from both the previous groups. They include solvency                   and bankruptcy models that predict the financial health of a company in the future.                   Another well-known indicator of this field is Economic Value Added. Hybrid                   indicators often use estimates and work with interest rates of government bonds. Their                   design is often complex, making them more difficult to interpret.                       The most common indicators used in the conducted economic studies include                   variously designed profitability (most frequently Return on Assets) and indicators                   based on revenues (Hult et al., 2008).","Castek_1_Castek  23.1.2015  7:37  Stránka 24                   24  2 COMPETITIVENESS AND ITS MEASUREMENT                     2.3 Financial performance indicators used                     We used the assumption that higher business performance is in the long run reflected                   in its profitability or growth in market share and the consequent growth of the company                   as such as the investigation by the Research Centre for the Competitiveness of the Czech                   Economy used when choosing the appropriate indicator to measure financial                   performance. The experienced authors of the most successful performance                   measurement system worldwide, the Balanced Scorecard method, comment: “Financial                   objectives typically relate to profitability – measured, for example, by operating income and                   return on investment. Basically, financial strategies are simple; companies can make more                   money by (1) selling more, and (2) spending less. Everything else is background music.                   ...Thus, the company's financial performance gets improved through two basic approaches                   – revenue growth and productivity.” (Kaplan and Norton, 2004, p. 36).                       The growth strategy usually consists of entering new markets and developing new                   products that require the introduction of additional production and service processes                   with which the company has not had substantial experience yet. An effort to                   standardize and streamline existing processes is the essence of the strategy to increase                   productivity, which is applied to activities usually performed for a longer period, in a                   familiar environment, and for well-known customers. Only excellent companies are                   able to implement both strategies at the same time, and thus achieve exceptionally                   high financial performance (Blažek et al., 2011).                       If we want to capture both possible strategies for achieving business performance,                   i.e. the growth strategy and the strategy of increasing productivity, it is necessary to                   use at least two indicators. However, a larger number of indicators used increases the                   time and cost of obtaining and processing data, and the amount of missing data                   increases as well. In addition, the combination of all indicators becomes more complex                   and more difficult to interpret. Therefore, it was decided to use two indicators, each                   of which will represent one of the two mentioned strategies.                       We decided to measure the strategy of increasing productivity, or profitability,                   using the indicator Return on Assets (ROA), which expresses the profitability of all                   resources in the company, regardless of their origin. This approach is in line with the                   stakeholder view of the company, used in the investigation of potential factors of                   performance; moreover, its result is not influenced by the type of capital structure of                   the company. ROA is one of the essential and most frequently used indicators of                   profitability (Richard et al., 2009). It was designed as follows:                        where:                   NOPBT – net operating profit before taxes                   TA – total assets                   t – year","Castek_1_Castek  23.1.2015  7:37  Stránka 25                                                            2.4 PERIOD OF PERFORMANCE MEASUREMENT  25                         The calculation uses operating profit, which is not affected by supplementary                   activities of the company and expresses its success on the market. Relating this value                   to the amount of assets gives the indicator an essential relative form, which allows the                   comparison of different-sized businesses.                       To capture the degree of implementing the growth strategy, we used the Assets                   Growth (AG) indicator. The rising value of the total assets and including a greater                   amount of resources at the same time is caused by the higher production of the                   company. During long-term growth in demand for its products, the company has to                   invest in expanding its production capacity, which increases the overall amount of                   assets. The second option is to select directly the indicator of sales growth, but it was                   not possible to calculate this indicator clearly from the database used (due to different                   procedures used in the database to determine the indicator of total sales, consisting                   in confusing total sales with revenues from the sale of goods, or products and services,                   total revenues or the performance indicator). The Assets Growth indicator was                   designed as follows:                        TA – total assets                   t – year                       2.4 Period of performance measurement                     We understand competitiveness as the ability of a company to operate on the market                   in the long term, sustainably in competition with other businesses. For this reason, it                   was necessary to measure business performance for a longer period of time. Using a                   time series also helps to reduce random fluctuations as well as intentional                   optimizations (such as creating reserves, etc.) in the performance of individual                   companies. From the perspective of corporate economy, a long period is understood                   to cover a period longer than 3 or 5 years. Even Krištof (2006) recommends following                   a five-year and longer series of indicators, with Kirby (2005) requiring an even longer                   period of about ten years. This requirement is based on the environment of North                   America, where a decade covers two terms of an executive director of a company on                   average. However, such research time may be too long in the current turbulent times.                   Factors applicable before this period may no longer be valid with such a considerable                   time interval. This is probably the reason why there are not many studies using a                   longer period than five years (e.g. Artiach (2010) – a five-year period, Abor (2007) –                   a six-year period, Hansen (1989) – a five-year period). On the other hand, many                   studies follow performance on the basis of only one-year results, e.g. Andrews (2010),                   Bottazzi (2008), Kessler (2007) and many others.","Castek_1_Castek  23.1.2015  7:37  Stránka 26                   26  2 COMPETITIVENESS AND ITS MEASUREMENT                         Another fundamental fact of our research aimed at finding competitiveness                   factors of a company is the existence of a time lag between the potential causes leading                   to increased performance and its actual rise. For this reason, it is first necessary to                   determine the possible factors of high performance and measure this performance                   subsequently. This ideally means determining the values of competitiveness factors                   in year 0 and then measure performance in years 1 to 10; moreover, we should allow                   for a delay in the publication of financial statements of the company. Nevertheless, it                   is not possible to postpone the analysis for so long due to the above-mentioned                   utilization of research findings in the current turbulent environment.                       Thus, it was necessary to examine a sufficiently long period of time, but at the                   same time not to delay the analysis too long after data collection. The questionnaire                   survey, which investigated the potential performance factors, was conducted in 2007.                   To analyse the performance, compromise was made: the time series of seven                   consecutive years for the period 2004–2010 was examined. The data for calculating                   financial performance for later years were not available for a sufficient number of                   companies at the time of the analysis, as entering financial data into the Albertina                   database and the Register of Companies is conducted gradually and with delay. Seven                   years is a sufficiently long period of time for inferring the long-term business                   performance. Even older data obtained from the extension of the time series                   backwards were no longer desirable due to a too long interval from the questionnaire                   survey.                     2.5 The development of performance measurement                        methodology                     Selecting two different indicators of financial performance led to the question of                   whether to analyse a company’s performance separately by ROA and separately by the                   Assets Growth, or whether to try to aggregate both the results into a single summary                   benchmark. The first approach is more common as it is used by approximately two                   thirds of economic studies, while aggregation of multiple indicators into one is used                   by approximately one third of studies (Richard et al., 2009). Given the purpose of the                   research, it was desirable for further analysis to group or sort the businesses within a                   single variable based on their financial performance. Only one performance indicator                   was required by the intended use of some special statistical methods. For this reason,                   we decided to merge the two indicators into a single one.                       Great attention was paid to finding the most appropriate way of analysing                   financial performance from the beginning of the previous research conducted by the                   Research Centre for the Competitiveness of the Czech Economy because it                   significantly determines the results of subsequent experiments. During the research,                   more possible solutions to the problem outlined were found and the model was revised                   and adjusted several times so that the selected indicator would reflect the real financial","Castek_1_Castek  23.1.2015  7:37  Stránka 27                                      2.5 THE DEVELOPMENT OF PERFORMANCE MEASUREMENT METHODOLOGY   27                     performance of the company as well as possible. Previous methods of ROA and Assets                   Growth aggregation into a single indicator are described in detail in the individual                   monographs summarizing the research conducted by the Research Centre for the                   Competitiveness of the Czech Economy (Blažek et al., 2008, 2009, 2011), and their                   comparisons are included in Pokorná and Částek (2013). Therefore, they will be only                   briefly described here.                    2.5.1 Cluster analysis                    In the first phase of finding methods for analysing business performance, Šiška (2008)                   first had to deal with the fact that finding the causes for higher business performance                   in the questionnaire survey, which was conducted in 2007, followed the time period                   for which it was possible to analyse the financial performance, i.e. 2002-2006.                   Although we can assume certain sluggishness in established business processes, it was                   appropriate to take into account the temporal distance of financial data in analysing                   business performance. Therefore, in order to reinforce the importance of financial                   data from the years closer to the empirical survey, he applied the weight of 1-2-3-4-5                   to both analysed indicators from 2002–2006. Thus, the weight was greatest for the                   latest data from 2006 and smallest for indicators from 2002. Besides weighing the data                   by years, they were also standardized using the z-score to eliminate the effects of                   different scales of both indicators.                       The first selected tool for analysing the financial performance was cluster analysis.                   Using 27 iterations of non-hierarchical k-means clustering, Šiška revealed 13 relatively                   homogeneous clusters associating a different number of businesses with similar values and                   development of ROA and Assets Growth over the five-year period analysed (graph 2-1).                     Graph 2-1: Clusters of cluster analysis                                         Source: Šiška, 2008","Castek_1_Castek  23.1.2015  7:37  Stránka 28                   28  2 COMPETITIVENESS AND ITS MEASUREMENT                         Distribution of companies in this number of groups made it considerably difficult                   to interpret the results and represented a problematic use in the subsequent statistical                   analysis. The clusters formed a categorical variable, which prevented a further                   statistical analysis using procedures requiring at least ordinal or cardinal variables.                   Therefore, this method was modified to cluster grouping based on the quadrant in                   which the clusters were located. This led to the creation of AA, AB, BA, BB and C                   groups (containing all clusters in areas marked with the letter C). Five categories of                   this variable proved more useful, but they still were not ordinal. With the need of at                   least an ordinal expression of financial performance, we used only businesses located                   in areas AA, BB and C. This made the dependent variable become a higher level                   variable (from categorical to ordinal); but it meant that the experiments could not                   include all businesses – businesses in the areas AB and BA were omitted. For these                   reasons, this method was not used further.                    2.5.2 Hyperbola                     In the next stage we were looking for a method to evaluate business performance,                   which would make it possible to put businesses into a small number of cardinal groups                   for the sake of interpretation – ideally only into two groups: companies economically                   successful and economically unsuccessful.                       When designing new methodology, Šiška assumed that the growth strategy and                   strategy of increasing productivity were mutually exclusive (Kaplan, Norton, 2004).                   This assumption was expressed in this methodology as an inverse proportion between                   the indicators used of ROA and Assets Growth. The product of the values of the two                   indicators represented a single-digit indicator of financial performance of a company,                   referred to as the coefficient of financial performance. When the value of one or two                   input variables was negative, i.e. a company was becoming smaller and/or depreciating                   its assets, the company was rated as economically unsuccessful regardless of the                   outcome of the mathematical product of both indicators.                       Ordering companies based on their performance was done using the coefficient                   of financial performance for the remaining businesses. A company can achieve the                   same financial performance for different strategies, e.g. if it weakens its focus on                   productivity and tries to get more customers instead, and expects that an increase in                   customers will lead to assets growth. We obtained the financial performance curve                   (graph 2-2) by connecting the points with the same values of the coefficient of financial                   performance but different combinations of ROA and Assets Growth values.                   Companies with a higher coefficient of financial performance are located on the higher                   financial performance curve.                       Companies located above the curve, which connected businesses with the                   financial performance coefficient of a median value, were identified as financially                   efficient; companies under the curve were marked as less financially efficient.                   Companies with a negative value of one or both indicators of financial performance,","Castek_1_Castek  23.1.2015  7:37  Stránka 29                                      2.5 THE DEVELOPMENT OF PERFORMANCE MEASUREMENT METHODOLOGY   29                     i.e. businesses from the second, third and fourth quadrant of graph 2-2, were marked                   as clearly inefficient. The name of the method – Hyperbola without weights – was                   derived from the geometric shape of the financial performance curves.                   Graph 2-2: Hyperbola                                              Source: Blažek et al., 2009                        Similarly to the previous method working with clusters, the indicator values used                   for calculating the financial performance coefficient were assigned weights reflecting                   the level of variable significance uniformly decreasing toward the past. In further                   research the authors stopped using the weights because their application caused large                   distortion (see experiments in the next chapter); thus, indicators for each year were                   assigned the same weight. This method was called Hyperbola with weights.                       Based on previous experience, Šiška (Blažek et al., 2009) tried to take into account                   the variability vs. stability of the results of companies in the next stage during the                   period analysed. He assumed that 1) a company with long-term stable values of                   financial indicators can probably face competition better than a company with the                   same average performance, which, however, strongly varies over time, and 2) all                   stakeholders consider a stable company, i.e. a low-risk company with balanced                   indicators, more attractive. Therefore, he purged risk from the average values of both                   financial indicators using a standard deviation. The calculation based on the method                   called  Risk-purged hyperbola for a six-year ROA average was as follows (and                   similarly for Assets Growth):","Castek_1_Castek  23.1.2015  7:37  Stránka 30                   30  2 COMPETITIVENESS AND ITS MEASUREMENT                         When searching for ways to refine the results obtained, the authors also                   considered and tested the possibility of rating business performance separately in each                   industry. The results of a method called Sector-hyperbola, however, failed to be more                   accurate than in previous methods (see section 2.6).                       The method variants with a hyperbola meet the criteria of a cardinal variable and                   a small number of the final business groups based on their performance; however, the                   explanation of the correlation between the two indicators, which was expressed as                   their product in the calculation of the financial performance coefficient, appeared                   problematic. This method of calculation provided a substantial undesirable distortion                   of business analysis, favouring those companies that pursued both strategies                   simultaneously (e.g. an average company with ROA 5% times Assets Growth 5% =                   financial performance coefficient of 25) compared to businesses that focused only on                   one of them although they achieved high success in this one strategy (e.g. ROA 15%                   times Assets Growth 1% = financial performance coefficient of 15). A fundamental                   problem was also assessing companies with zero Assets Growth and high profitability,                   and vice versa, as inefficient due to multiplication of a large number by zero. For these                   reasons, the method was subsequently used only as a dichotomous variable that                   separated businesses to those that were found above the hyperbola (successful) and                   those that were found below the hyperbola (unsuccessful). To highlight the differences                   between these two categories, borderline businesses, located in close proximity to the                   hyperbola, were omitted for some experiments. Typically, these were 5% of companies                   above and 5% of companies below the hyperbola. In graph 2-2 these borderline                   businesses are identified as Group AB. This made it possible to overcome the                   aforementioned drawbacks; however, the variable could not be used as a cardinal                   variable.                     2.5.3 Summation                    In further search for an appropriate methodology, we took into account the                   shortcomings of the previous methods. The output was still expected to be a                   continuous variable or a discrete ordinal variable with fine resolution, which could                   subsequently be divided into a small number of company groups based on financial                   performance.                       When working with two indicators it was again necessary to convert the values                   of ROA and Assets Growth to the same scale. We used the method of standardization,                   which preserves the information value of the resulting z-score compared to                   normalization.                       In the design of a single-digit indicator, we put emphasis on the equivalence of                   the growth strategy and the strategy of increasing productivity, including any possible                   combination of these two strategies in achieving performance. Therefore, the                   standardized indicators of ROA and Assets Growth are of the same weight and they                   can be simply added up without the risk of distortion. This method eliminates the","Castek_1_Castek  23.1.2015  7:37  Stránka 31                                      2.5 THE DEVELOPMENT OF PERFORMANCE MEASUREMENT METHODOLOGY   31                     aforesaid problems associated with the hyperbola method. The resulting financial                   performance coefficient is a one-dimensional variable, which can be graphically                   represented with a curve. In the following text, this method is referred to as                   Summation.                       A variant of the summation method is the  Exponent method, which we                   considered and in which we also tried to highlight the differences between companies                   using a power relationship between the variables:                        where a>1.                        Variable a that influences the degree of variance of the financial performance                   coefficient was arbitrarily set as a=2 in further experiments.                     2.5.4 Quintiles                    Another method was designed by J. Šiška and M. Králová (2012). They operate with                   a graphical representation of indicators on the two main axes, similarly to the                   hyperbola or cluster method (Fig. 2-3). They divided the resulting space of the upper                   right quadrant in particular into several segments and assigned each segment points                   expressing a company’s performance.                       Figure 2-3: Quintiles method                                          Source: Pokorná, Částek, 2013, modified according to J. Šiška and Králová, 2012","Castek_1_Castek  23.1.2015  7:37  Stránka 32                   32  2 COMPETITIVENESS AND ITS MEASUREMENT                         We adjusted the proposal to our needs by changing the boundaries between the                   segments. The lowest score was assigned to companies that represent up to 5% of the                   sample for both indicators; on the other hand, the highest score was assigned to                   companies that belong in the top 5% in both indicators. We separated the remaining                   space between the two segments by quintiles. This method satisfies the ordinal variable                   requirement although its significant disadvantage is a subjective determination of the                   boundaries between the individual segments. Due to a large number of categories we                   can consider the variable quasi-interval.                     2.6 Assessing the appropriateness of methods to measure                        financial performance                     As seen in the previous section, there are several options in dealing with the selected                   indicators so that the result would be a one-dimensional variable. Unfortunately, from                   a theoretical point of view it is not possible to justify one of these options as better                   than others. Therefore, we decided to use experiments based on the following                   assumptions:                       1. there is a statistically measurable correlation between the factors analysed of                          competitiveness and financial performance,                       2. if the factors and the method used to measure correlation (association,                          tightness, determination) remain unchanged, then the value of the correlation                          coefficient for different representations of financial performance (association,                          tightness, determination) will represent the degree determining the                          appropriateness of the selected expression of financial performance.                       Should the aforementioned be true, it is necessary to choose a suitable method                   of measuring correlations. It is important that such a method in particular:                       1. is not affected by the shape of tightness (e.g. by linearity as correlation),                          because this shape can change if the expression of financial performance is                          changed,                       2. does not assume an a priori model (e.g. structural modelling), which would                          need to be changed when expressing financial performance,                       3. is able to measure the impact of several independent variables with possible                          interdependencies.                       For the above reasons, it is therefore possible to exclude the majority of the                   commonly used methods from application: correlation, linear regression, structural                   modelling, decision trees, partially methods of multiple regression and multiple                   correlation. On the contrary, these shortcomings are not present in the selected                   algorithm of sequential floating forward selection (SFFS) in combination with the k-                   Nearest Neighbours classification method, presented in next chapters. It should be                   pointed out that the SFFS algorithm reduces the set of so-called symptoms; in our                   case, these are the variables describing businesses so as to preserve the most","Castek_1_Castek  23.1.2015  7:37  Stránka 33                        2.6 ASSESSING THE APPROPRIATENESS OF METHODS TO MEASURE FINANCIAL PERFORMANCE  33                     informative symptoms, i.e. variables contributing most to separating companies into                   classes. We understand classes as categories of financial performance. This process                   therefore requires that the variable analysed is categorical, which was convenient in                   our situation as all types of financial performance evaluation proposed in the previous                   section could be converted to a categorical variable, while variables with a lower level                   of quantification could not be converted for example to a cardinal variable if required.                   For methods that produced cardinal variables, we separated the companies into two                   classes, i.e. above average and below average, while omitting about 10% of borderline                   businesses in order to distinguish better more competitive ones from less competitive                   ones.                     2.6.1 Experiment settings                    To evaluate the informativeness of the tested variable sets, we used the classification                   method of k-Nearest Neighbours, which groups samples (companies) into individual                   classes (categories of importance) by k of the nearest neighbours. The number of                   nearest neighbours k is therefore an optional parameter of the experiments. Since it                   is not possible to clearly decide what size of k should be used, the experiments were                   carried out separately with k set to 1, 3 and 5. Even values are not usually used in order                   to avoid undecided situations (Blažek et al., 2008, pp. 48–49). On the other hand, the                   number of companies in the individual categories of importance is too low for a value                   greater than 5. After each experiment, the authors chose the size of k that helped reach                   the most informative variable set as the most suitable. The same procedure was used                   in the search for competitiveness factors (Blažek et al, 2008, p. 89). In the following                   text, the individual k’s used will be referred to as methods 1NN, 3NN and 5NN.                       Each company was described with 37 variables representing potential competi-                   tiveness factors, referred to as “symptoms” in the terminology of statistical pattern                   recognition. More information about working with these variables before the                   application of statistical methods and about the SFFS algorithm can be found in the                   article on the benefits of this algorithm in the search for competitiveness factors                   (Špalek, Částek, 2010).                     2.6.2 Experiment output                    The table below shows the descriptive statistics of informativeness values obtained                   using different methods of analysing financial performance. The methods are ranked                   on the basis of average informativeness values achieved. It is clear that the                   performances produced by the first three methods differ within three per thousand,                   while the fourth method lags behind the best one by almost two percentage points.                   Hence, the most accurate method seems to be summation, followed by hyperbola                   without weights and the exponent method closely trailing.","Castek_1_Castek  23.1.2015  7:37  Stránka 34                   34  2 COMPETITIVENESS AND ITS MEASUREMENT                     Figure 2-4: Descriptive statistics of informativeness values produced by different methods                      Fin. perf. measurement method  Minimum  Maximum      Mean    Std. Devia on                     Summa on                     0.739       0.782       0.765       0.022                     Hyperbola without weights    0.747       0.787       0.762       0.022                     Exponent                     0.751       0.773       0.761       0.011                    Quin les                     0.745       0.751       0.749       0.003                     Hyperbola with weights       0.730       0.755       0.744       0.012                     Sector hyperbola             0.709       0.725       0.717       0.008                     Risk‐purged hyperbola        0.701       0.715       0.706       0.008                          However, besides informativeness, we can use other criteria to assess the efficiency                   of methods. One of them can be the rate of fluctuation for selected variables. In the                   next table, we can see how the SFFS algorithm output can be summarized. It lists the                   values of informativeness, the number of variables in the set of variables with the                   highest informativeness, and variable codes contained in this most informative set for                   classifiers 1NN, 3NN and 5NN.                      Figure 2-5: Summary of the SFFS algorithm output for the exponent method                                            Proper es of the most informa ve variable subset                     Classifier                                Informa veness  Number of variables        Variables                      1NN                                  0.750685             9         3 7 9 14 18 31 32 33 34                      3NN         0.772603             13        4 5 12 14 19 24 25 26 27 31 34 35 36                       5NN         0.758904             4         8 9 14 17                     Note:   bold – variables selected once                          italics – variables selected twice                          underlined – variables selected always","Castek_1_Castek  23.1.2015  7:37  Stránka 35                        2.6 ASSESSING THE APPROPRIATENESS OF METHODS TO MEASURE FINANCIAL PERFORMANCE  35                         Ideally, not only should the value of informativeness be high, but different                   classifiers should also agree on the same variables. However, in the case of the                   exponent method we see that all three methods selected only one variable, which is                   number 14, three variables were selected twice (9, 31, 34), but seventeen variables                   were selected only once. To compare it with the other methods, we can design the                   following analysis of variable fluctuations in the most informative set:                       where number of items is the sum of the selected variables; so for the above mentioned                   case the number of different variables is 1 (number 14) + 3 (numbers 9, 31 and 34) +                   17 (other variables) divided by the Number of items, i.e. 9 + 13 + 4, and divided by                   three (because every time the experiment was conducted for 1NN, 3NN and 5NN).                   The formula would look as follows:                            This means that the result equals 1.52; in fact, the result can range within the                   interval from zero to two, with zero being the lowest fluctuation (every kNN selects                   the same variables) and 2 meaning the maximum fluctuation (each kNN selects a                   completely different variable). Fluctuation in this case is actually the equivalent of                   generalizability: if it is low, we can expect the same result with higher probability in                   multiple repetitions with a random variable. The table below shows the average data                   on the most informative variable sets.                    Figure 2-6: Fluctuation analysis                                                                Average values                    Fin. perf. measurement method                                                                        Number of variables in the                                              Informa veness  Fluctua on                                                                         most informa ve subset                    Summa on                     0.765        1.25                  4.00                     Hyperbola without weights    0.762        1.54                  8.67                    Exponent                     0.761        1.52                  8.67                     Quin les                     0.749        1.18                 16.00                     Hyperbola with weights       0.744        1.02                 15.33                    Sector hyperbola             0.717        1.36                  4.67                     Risk‐purged hyperbola        0.706        0.80                  3.33","Castek_1_Castek  23.1.2015  7:37  Stránka 36                   36  2 COMPETITIVENESS AND ITS MEASUREMENT                           Let us assume, like in the case of informativeness, that if the experiment setting                   is the same and differs only in the method used to divide the companies, lower                   fluctuation of selected variables means that the applied method divides the businesses                   better. Then we can better identify the success of the best three methods assessed for                   analysing financial performance, whose informativeness value is very similar. The                   method of summation, which had the highest informativeness value, is foremost                   among these three methods even from the perspective of the fluctuation criterion.                   The difference against the hyperbola without weights and the exponent method is now                   much stronger than it was for informativeness. The choice of the summation method                   can be further confirmed by the average number of selected variables in the most                   informative set, which is less than a half for the summation method compared to the                   hyperbola without weights and exponent methods. For summation, the kNN                   classifiers identified a set of six variables one time and a set of three variables two                   times (i.e. 9 different variables) as most informative, while for the hyperbola without                   weights it was six, sixteen and four variables (i.e. 22 different variables), and for the                   exponent method it was nine, thirteen and four variables (i.e. 21 different variables).                   In the latter two cases, more than half of the input variables were selected as most                   informative.                       Given the results of the experiments and other advantages of the summation                   method (e.g. problem-free work with negative values compared to methods based on                   a hyperbola), the summation method was selected for further utilization.                     2.7 Description of the methodology used to measure                        performance                     To analyse the performance, the ROA and Assets Growth indicators were used for a                   7-year period from 2004 to 2010. Both the indicators were calculated from data                   obtained from the Albertina CZ database, which contains data from the financial                   statements of companies registered in the Czech Republic. Yet, there were missing                   data in the database that had to be found in other publicly available data sources (such                   as the Register of Companies, digitized volumes of the Commercial Bulletin, or the                   Albertina database). Even after this manual completion of the database, some data                   were still missing. As for the ROA indicator, we accepted a maximum of two missing                   figures from the seven-year time series; due to their volatile development in time they                   were not replaced with the average values for the company or for all companies in a                   given year, but the indicator value was not calculated for the year with the missing                   data. As a result, the overall ROA value was averaged for the number of years for which                   it was possible to calculate the indicator (i.e. for a minimum of 5 years in the case of                   2 missing figures). As for the Assets Growth indicator, we evaluated those companies                   whose Assets Growth indicator could be calculated for at least 5 years from the period","Castek_1_Castek  23.1.2015  7:37  Stránka 37                                     2.7 DESCRIPTION OF THE METHODOLOGY USED TO MEASURE PERFORMANCE   37                     analysed of 2004–2010. In practice, however, this criterion did not change the number                   of un-/analysed businesses: it was possible to calculate Assets Growth for all businesses                   for which it was possible to calculate the ROA. The analysis of financial performance                   was conducted for 411 companies out of 432; in the case of the remaining 21                   companies, too many figures were missing.                       Some companies from the basic sample showed an increase in Assets Growth by                   as much as tens of thousands of a per cent for the observed seven-year period. This                   increase, however, cannot be considered a long-term success of a company in its                   growth strategy, since according to the data from the Register of Companies these                   were mostly newly established businesses, or companies which were involved in a                   merger in the given year, etc. To prevent such extreme values from distorting the                   results of the financial analysis, the data on Assets Growth were adjusted so that values                   above 1000% were disregarded and replaced with an empty value. Such companies                   did not occur in the selected sample. As for the businesses from the sample that lacked                   (a maximum of 2) figures representing the amount of total assets at the end of the                   period analysed, these values were replaced with a value that equalled the value from                   the previous year increased by the average Assets Growth of the basic sample in a                   given year. Analogously, the missing values for the beginning of the period were                   replaced with the total assets value in the following year, reduced by the average Assets                   Growth in a given year. This adjustment affected 47 companies from the selected                   sample. In the case of the ROA indicator, the annual values above 200% and below                   -200% were replaced with an empty value.                       For the purpose of further data processing, it was necessary to use the same scale                   for the values of both financial indicators. Standardization was conducted using the                   following formula:                         where i=(1, 2, 3, 4, 5, 6, 7) for ROA and the mean value in the formula is the median                   of the whole population calculated for each year separately from the Albertina CZ                   database, and the standard deviation is a deviation of the whole population for each                   year separately. We eliminated the influence of different economic developments in                   individual years by using the standardizations for every year. The resulting value of                   the ROA indicator for one company is then the arithmetic average of seven                   standardized values.                       The Assets Growth indicator for 7 years represents the standardized geometric                                                      2                   mean for the seven-year period of 2004 –2010. The geometric mean is usually used                   to calculate the average growth rate.                     2  The seven-year average of Assets Growth is based on the values of total assets for 2003 and 2010, as the                     initial value of total assets for 2004 equals the final value of total assets for 2003.","Castek_1_Castek  23.1.2015  7:37  Stránka 38                   38  2 COMPETITIVENESS AND ITS MEASUREMENT                     The geometric average of Assets Growth:                          TA – Total Assets                        Standardization was conducted similarly to ROA; the difference was that only                   one value per company (geometric Assets Growth 2004-2010) was standardized.                       Using standardization retains the explanatory power of z-score: z-score equals                   zero for an average company. In the case of the normal distribution, the standardized                   value of ROA (or Assets Growth) for 68.26% of companies is in the range of <-1; 1>.                   There are only 13.59% of companies with the standardized ROA value above 1.00,                   while companies whose value of the standardized ROA is above 2.00 belong to the                   exceptionally performing businesses; there are only 2.14% of equally good or better                   companies.                       Converting values of both indicators to a single scale using standardization makes                   it possible to compare the extent of implementing the growth strategy and the strategy                   of increasing productivity, which are regarded as equivalent. Using the above-                   mentioned method of summation, i.e. a simple summing up of both the standardized                   indicators, we obtained the desired one-dimensional coefficient of financial                   performance, which indicates the performance of a company regardless of the strategy                   chosen. This methodology marks companies whose financial performance coefficient                   is greater than 0 as above average; this means that the higher the coefficient is, the                   more efficient a company is (and vice versa). Businesses that notably increase in size                   (Assets Growth > 0) while showing average profitability (z-score for ROA = 0) will be                   marked as above-average as well; this is also true for companies whose productivity                   is substantially increasing (ROA > 0) while showing an average growth (z-score for                   Assets Growth = 0), or they are above-average in both strategies at the same time (z-                   score for both indicators > 0). A company that is becoming smaller in the long term                   may not yet be included among inefficient businesses if the standardized rate of its                   profitability is higher than the standardized rate of its (negative) growth (i.e. a situation                   where the absolute value of the negative z-score for Assets Growth is smaller than the                   absolute value of the positive z-score for ROA).","Castek_1_Castek  23.1.2015  7:37  Stránka 39                                                                                                   39                               3 Feature Selection Methods in Statistical Pattern                       Recognition                          3.1 Introduction                     With the ever-increasing specialisation and diversification of scientific disciplines, it                   is common that similar problems are being tackled in other branches of science,                   usually without an awareness of the respective research and application communities.                   It is just this case where the methods developed in a relatively distant field of statistical                   pattern recognition (SPR) can be used to solve the earlier defined problem of                   identifying factors of corporate competitiveness, a problem from the field of business                   and management. Statistical pattern recognition is a discipline comprised of analytical                   and adaptive methods for processing large datasets, selecting useful information aimed                   at reducing the data dimensionality and finally classifying these data. Pattern                   recognition is actually closely connected with machine learning and therefore it is                   considered to belong to the field of artificial intelligence. One of the fundamental                   problems of statistical pattern recognition is representing patterns in a reduced                   number of dimensions, which means a dimensionality reduction. The methods of                   feature selection are used in statistical pattern recognition to solve this task.                       As the methods of statistical pattern recognition represent the essential part of                   our methodology used for solving the research problems specified in the project, we                   consider devoting a special chapter to presenting their fundamentals important.                       A broad class of decision-making problems can be solved by the  learning                   approach. This can be a feasible alternative when neither an analytical solution exists                   nor the mathematical model can be constructed. In these cases the required                   knowledge can be gained from the past data, which form the so-called “learning” or                   “training set”. Then, the formal apparatus of statistical pattern recognition can be used                   to learn the decision-making. The first and essential step of statistical pattern                   recognition is to solve the problem of variable (feature) selection or more generally                   of dimensionality reduction, which can be accomplished either by a linear or nonlinear                   mapping from the measurement space to a lower dimensional feature space.","Castek_1_Castek  23.1.2015  7:37  Stránka 40                   40  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                         We will examine some of the most popular tools under various settings to point                   out several pitfalls often omitted in current literature. In the following we will prefer                   the term feature selection to variable selection in accordance with statistical pattern                   recognition conventions.                     3.1.1 Common Research Issues in Machine Learning and Management                    Though managers, economists and researchers or practitioners from other fields have                   different priorities in research issues, issues common to both the fields exist. Such an                   issue is the problem of selecting only that information which is necessary (and if                   possible also sufficient) for decision-making. We strongly believe that statistical                   pattern recognition is the discipline capable of providing a common methodology.                       A typical problem which managers often encounter is the problem of too many                   potential inputs into their respective decision-making problems. This phenomenon                   has been extensively studied in mathematics and in artificial intelligence. The “curse                   of dimensionality” problem, as coined by the famous American mathematician                   Richard Bellman, can perhaps be found in all the fields of science and application                   areas including economics and management. Without going into the details of this                   phenomenon, it can be stated that in order to make reliable decisions (or more exactly,                   to learn to make them based on past experience and the available data) the need for                   the amount of data dramatically grows with the number of inputs. Mathematically it                   means that the sample size required grows exponentially with the data dimensionality.                   This problem is very relevant particularly to the field of management and economics,                   as the process of managerial or economic data acquisition is usually both time-                   consuming and costly. Consequently, the data sets acquired are usually too small with                   respect to their dimensionality.                       Though managers consider their respective problems to be of a somewhat                   different nature (perhaps understandably from their professional point of view), from                   the point of view of mathematics, the same problem exists formally. It is just a question                   of different terminology and abstraction needed to find a unified look at the problem.                   Let us just give an example what we mean by considering which sets of inputs                   managers use for their decision-making: economic indices, financial data, time series,                   prediction estimates, etc.                       For a mathematician, however, these sets can be looked upon as a set of variables,                   forming the input vector (in pattern recognition which deals with this problem the                   term feature vector is used). In the majority of practical cases, the dimensionality (the                   number of inputs) of the original input space can be rather high. It is just a natural                   consequence of the well-known fact that in the design phase of any system for                   supporting decision-making, it is extremely difficult or practically impossible to                   evaluate directly the “usefulness” of particular input variables.                       Managers certainly face this problem many times, when having to make the                   decision. For instance, a manager could have a large number of economic variables","Castek_1_Castek  23.1.2015  7:37  Stránka 41                                                                       3.2 DIMENSIONALITY REDUCTION  41                     to potentially consider for performing a multiple regression analysis (too many                   potential regressors). Yet, owing to the often very complex relations and dependencies                   (sometimes rather strong) among all the respective inputs, economic variables exist                   (let us speak generally just about variables) which can be left out from decision-                   making without a great loss of information content. The theory of information, a                   special mathematical discipline, defines this as the existence of “redundancy” in the                   set of variables. However, even if managers were aware of this phenomenon, the                   problem of solving the task of finding the redundant variables for complex problems                   with many potential inputs would be beyond human capabilities.                       The reasons for trying to reduce the set of our inputs into the decision-making                   process by eliminating redundancies have both practical and theoretical foundations.                   The practical ones perhaps do not need to be discussed – the reduced cost of the data                   acquisition is sufficient to substantiate the reduction. On the theoretical front we                   should like to mention a famous theorem by another American mathematician, S.                   Watanabe. He founded the mathematical theory of cognition by paraphrasing a world-                   known fairy tale by the Norwegian author Hans Christian Andersen, where he                   formulated “the ugly duckling theorem”. Roughly stated, it says that no cognition is                   possible unless our perceptions (input variables) are weighted and, consequently, many                   of them are given a null weight and thus eliminated from the cognition process.                       Each of the fields considered (managerial and clinical decision-making) has its                   own specificity, and accordingly, different ways of treating the problem. On the other                   hand, with the ever-increasing specialization and diversification of scientific                   disciplines, it is not an uncommon fact that similar problems are being tackled in                   other branches of science, usually without the awareness of respective research and                   application communities. Yet the results and methods from one scientific discipline                   can be applied not only to solve problems in another quite different discipline, but                   they can also often enrich its methodology.                       It is our belief that novel methods developed recently in the field of statistical                   pattern recognition to solve the problem of feature selection can enrich the                   methodology of selecting the most useful information for decision-making problems                   in management. Conversely, solving these problems can enrich the methodology of                   statistical pattern recognition and feature selection.                     3.2 Dimensionality Reduction                                                                                            D                   We shall use the term “pattern” to denote the D-dimensional data vector x ∈ X ⊆ R of                   measurements, the components of which are the measurements of the features of the entity                   or object. We also refer to x as the feature vector. Let Y = { f , • • • , f |Y|  } be the set of D =                                                                    1                   |Y| features, where |•| denotes the size (cardinality). The features are the variables specified                   by the investigator. Following the statistical approach to pattern recognition, we                   assume that a pattern x is to be classified into one of a finite set of C different classes","Castek_1_Castek  23.1.2015  7:37  Stránka 42                   42  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                     Ω = {ω , ω ,…, ω }. A pattern x belonging to class wi is viewed as an observation of                             2                         1                                  C                   a random vector  X drawn randomly according to the known class-conditional                   probability density function p(x|ω ) and the respective a priori probability P(ω ).                                                                                        i                                                 i                       One of the fundamental problems in statistical pattern recognition is representing                   patterns in a reduced number of dimensions. In most practical cases, the pattern                   descriptor space dimensionality is rather high. It follows from the fact that it is too                   difficult or impossible to evaluate directly the “usefulness” of particular input in the                   design phase. Thus, it is important to initially include all the “reasonable” descriptors                   the designer can think of and reduce the set later on. Obviously, information missing                   in the original measurement set cannot be substituted later. Dimensionality reduction                   (DR in the following) is an important step in data pre-processing in pattern                   recognition and machine learning applications. In general, it can be shown that such                   tasks as classification or approximation of the data represented by so-called “feature                   vectors”, can be carried out in the reduced space, more accurately than in the original                   space, as demonstrated by the so-called “Peaking Phenomenon” (see Fig. 3-7).                       The aim of dimensionality reduction is to find a set of new d features based on                   the input set of D features (if possible d<<D), so as to maximize (or minimize) an                   adopted criterion.                    DR Categorization According to Nature of the Resulting Features                    There are two main distinct ways of viewing DR according to the nature of the                   resulting features:                       –DR by feature selection (FS)                       –DR by feature extraction (FE).                       The FS approach does not attempt to generate new features, but to select the “best”                   ones from the original set of features. Depending on the outcome of a FS procedure,                   the result can be a set of weighting-scoring, a ranking or a subset of features. The FE                   approach defines a new feature vector space in which each new feature is obtained by                   combinations or transformations of the original features (see Figs. 3-8a; 3-8b).                       FS leads to savings in measurements cost since some of the features are discarded and                   the selected features retain their original physical or economic interpretation. On the other                   hand, transformed features generated by feature extraction may provide a better                   discriminative ability than the best subset of given features (gained by FS), but these new                   features may not have a clear physical or economic meaning and interpretation.                    DR Categorization According to the Aim                    DR can be alternatively divided according to the aim of the reduction:                       –DR for optimal data representation                       –DR for classification.                       The first aims to preserve the topological structure of data in a lower-dimensional                   space as much as possible, while the second one aims to enhance the subset of","Castek_1_Castek  23.1.2015  7:37  Stránka 43                                                                       3.2 DIMENSIONALITY REDUCTION  43                     Figure 3-7: Peaking Phenomenon – correct classification rate is a nonmonotonous function of the                   number of features                                           Figure 3-8a: Scheme of FS                                       Figure 3-8b: Scheme of FE","Castek_1_Castek  23.1.2015  7:37  Stránka 44                   44  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                     discriminatory power. Although the same tools may be often used for both purposes,                   caution is needed. An example is Principle Component Analysis, one of the primary                   tools for representing data in lower-dimensional space, which may easily discard                   important information if used for DR for classification. In the following we shall                   concentrate on the feature subset selection problem only, with classification being the                   primary aim. For a broader overview of the subject, see Duda et al. (2000), McLachlan                   (2004), Ripley (2005), Theodoridis et al. (2006), or Webb (2002), for example.                      3.3 Feature Subset Selection                     Given a set Y of |Y| features, let us denote X the set of all possible subsets of size d,                                                          d                   where d represents the desired number of features. Let J(X) be a criterion function                   that evaluates the feature subset X ∈ X . Without any loss of generality, let us consider                                                    d                   a higher value of J to indicate a better feature subset. Then the feature selection                   problem can be formulated as follows:                                     ~                                                  ~                       Find the subset X for which J(X d ) = max J(X).              (1)                                      d                                                     X∈X d                       Assuming that a suitable criterion function has been chosen to evaluate the                   effectiveness of feature subsets, feature selection is reduced to a search problem that                   detects an optimal feature subset based on the selected measure. Note that the choice                   of d may be a complex issue depending on problem characteristics, unless the d value                   can be optimized as part of the search process.                       One particular property of feature selection criterion, the monotonicity property,                   is required specifically in certain optimal FS methods. Assuming we have two subsets                   S and S of feature set Y and a criterion J that evaluates each subset S , the                           2                                                                                        i                    1                   monotonicity condition requires the following:                                              S ⊂ S ⇒ J(S ) ≤ J(S ).                (2)                                               1                                                   2                                                         1                                                                2                       That is, evaluating the feature selection criterion on a subset of features of a given                   set yields a smaller value of the feature selection criterion.                   3.3.1 FS Categorization With Respect to Optimality                   Feature subset selection methods can be split into basic families:                   •   Optimal methods: These include exhaustive search methods, for instance, which                       are feasible only for small sized problems and accelerated methods, mostly based                       on the Branch \& Bound principle (Somol et al., 2004). All optimal methods can                       be expected to be considerably slow for problems of high dimensionality.                   •   Sub-optimal methods: They essentially trade the optimality of the selected subset                       for computational efficiency. They include, e.g., Best Individual Features, Random                       (Las Vegas) methods, Sequential Forward and Backward Selection, Plus-l-Take                       Away-r, their generalized versions, genetic algorithms, and the Floating and","Castek_1_Castek  23.1.2015  7:37  Stránka 45                                                                        3.3 FEATURE SUBSET SELECTION  45                         Oscillating algorithms in particular (Devijver et al., 1982; Pudil et al., 1994; Somol                       et al., 2000; Somol et al., 2008b).                        Although an exhaustive search guarantees the optimality of a solution, in many                   realistic problems it is computationally prohibitive. The well-known Branch and                   Bound (B\&B) algorithm guarantees selecting an optimal feature subset of size d                   without involving explicit evaluation of all the possible combinations of d                   measurements. However, the algorithm is applicable only under the assumption that                   the feature selection criterion used satisfies the monotonicity condition (2). This                   assumption precludes the use of the classifier error rate as the criterion (cf. wrappers,                   Kohavi et al. (1997)). This is an important drawback as the error rate can be considered                   superior to other criteria, Siedlecki et al. (1993), Kohavi et al. (1997), Tsamardinos et                   al. (2003). Moreover, all optimal algorithms become computationally prohibitive due                   to their problems of high dimensionality. In practice, therefore, one has to rely on                   computationally feasible procedures which perform the search quickly but may yield                   sub-optimal results. A comprehensive list of sub-optimal procedures can be found in                   Devijver et al. (1982), Fukunaga (1990), Webb (2002) and Theodoridis et al. (2006)                   among others. A comparative taxonomy can be found in Blum et al. (1997), Ferri et                   al. (1994), Guyon et al. (2003), Jain et al. (1997), Jain et al. (2000), Yusta (2009), Kudo                   et al. (2000), Liu et al. (2005), Salappa et al. (2007), Vafaie et al. (1994) or Yang et al.                   (1998). Our own research and experience with FS has led us to the conclusion that no                   unique generally applicable approach to the problem exists. Some approaches are more                   suitable under certain conditions; others are more appropriate under other conditions,                   depending on our knowledge of the problem. Hence, continuing effort is being invested                   in developing new methods to cover the majority of situations which can be                   encountered in practice.                     3.3.2 FS Categorization With Respect to Selection Criteria                    Based on the selection criterion choice, feature selection methods may roughly be                   divided into:                   •   Filter methods (Yu et al., 2003; Dash et al., 2002) are based on performance                       evaluation functions calculated directly from the training data such as distance,                       information, dependency, and consistency, and select feature subsets without                       involving any learning algorithm.                   •   Wrapper methods (Kohavi et al., 1997) require one predetermined learning                       algorithm and use its estimated performance as the evaluation criterion. They                       attempt to find features better suited to the learning algorithm aiming to improve                       performance. Generally, the wrapper method achieves better performance than                       the filter method, but tends to be more computationally expensive than the filter                       approach. Also, wrappers yield feature subsets optimized for the given learning                       algorithm only – the same subset may thus be unsuitable in another context.","Castek_1_Castek  23.1.2015  7:37  Stránka 46                   46  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                     •   Embedded methods (Guyon et al., 2003, but also Kononenko, 1994 or Pudil et al.,                       1995; Novovičová et al., 1996) integrate the feature selection process into the                       model estimation process. Thus, devising a model and selecting its features is one                       inseparable learning process that may be looked upon as a special form of                       wrappers. Therefore, embedded methods offer performance competitive to                       wrappers, enable a faster learning process, but produce results tightly coupled                       with the particular model.                   •   The  Hybrid approach (Das, 2001; Sebban et al., 2002; Somol et al., 2006) combines                       the advantages of more than one of the approaches listed. Hybrid algorithms have                       recently been proposed for dealing with high dimensional data. These algorithms                       mainly focus on combining filter and wrapper algorithms to achieve the best                       possible performance with a particular learning algorithm, with the time                       complexity comparable to that of the filter algorithms.                    3.3.3 FS Categorization With Respect to Problem Knowledge                     From another point of view there are perhaps two basic classes of situations with                   respect to a priori knowledge of the underlying probability structures:                   •   Some a priori knowledge is available: it is at least known that probability density                       functions are unimodal. In these cases, one of probabilistic distance measures                       (Mahalanobis, Bhattacharyya, etc., see Devijver et al. (1982)) may be appropriate                       as the evaluation criterion. For these types of situations we recommend either the                       recent prediction-based B\&B algorithms for optimal search Somol et al. (2004), or                       sub-optimal search methods in an appropriate filter or wrapper setting (Sect. 3.4).                   •   No a priori knowledge is available: we cannot even assume that probability density                       functions are unimodal. For these situations, either a wrapper-based solution                       using sub-optimal search methods (Sect. 3.4) can be found suitable, or, provided                       the size of training data is sufficient, it is possible to apply one of the embedded                       mixture-based methods that are based on approximating unknown class-                       conditional probability density functions by finite mixtures of a special type                       (Pudil et al., 1995; Novovičová et al., 1996).                      3.4 Sub-optimal Search Methods                     Provided a suitable FS criterion function has been chosen, feature selection is reduced                   to a search problem that detects an optimal feature subset based on the selected                   measure. Then the only tool needed is the search algorithm that generates a sequence                   of feature subsets to be evaluated by the respective criterion (see Fig. 3-9).                       Despite advances in optimal search (Somol et al., 2004; Nakariyakul et al., 2007),                   we have to resort to sub-optimal methods for larger than moderate-sized problems,                   of which a very large number of various methods exist.","Castek_1_Castek  23.1.2015  7:37  Stránka 47                                                                    3.4 SUB-OPTIMAL SEARCH METHODS  47                     Figure 3-9: Feature selection algorithms can be viewed as black box procedures generating a                   sequence of candidate subsets with respective criterion values, among which intermediate solutions                   are chosen.                                               Figure 3-10: In this 2D case nor feature 1 nor 2 is sufficient to distinguish patterns from classes of                   rectangles and circles. Only when information from both features is combined, classes can be                   separated (dotted line)","Castek_1_Castek  23.1.2015  7:37  Stránka 48                   48  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                         In the following, we present a basic overview over several tools that are useful for                   problems of varying complexity, based mostly on the idea of sequential search (Section                   4.2). An integral part of any FS process is the decision about the number of features                   to be selected. Determining the correct subspace dimensionality is a difficult problem                   beyond the scope of this chapter. Nevertheless, in the following we will distinguish                   two types of FS methods: d-parametrized and d-optimizing. Most of the available                   methods are d-parametrized, i.e., they require the user to decide what cardinality the                   resulting feature subset should have.                    3.4.1 Best Individual Features                    The Best Individual Features (BIF) approach is the simplest approach to FS. Each                   feature is first evaluated individually using the chosen criterion. Subsets are then                   selected simply by choosing the best individual features. This approach is the fastest                   but weakest option. It is often the only applicable approach to FS in problems of very                   high dimensionality. BIF is standard in text categorization (Yang et al., 1997;                   Sebastiani, 2002), and genetics (Xing, 2003; Saeys et al., 2007), etc. BIF may be                   preferable in other types of problems to overcome FS stability problems (see Sect. 6.1).                   However, it completely ignores inter-feature relations and as such can not reveal                   solutions, where combinations of features are needed (see Fig. 3-10).                       It should be noted that BIF is often considered the method of choice when the                   problem to be solved is difficult due to unfavourable properties of training data. The                   fact that BIF has limited optimization power becomes an advantage, e.g., with very                   high-dimensional data and/or with low-sample size data. See Sect. 6 for more                   discussion of the problem of overfitting, which in fact is not uncommon in economics                   where high data acquisition cost and privacy issues often prevent practitioners from                   obtaining large enough training sets.                    3.4.2 Sequential Search Methods and their Evolution                    More advanced methods that take into account relations among features are likely to                   produce better results. Several such methods are discussed in the following.                       When feature relations are taken into account, the basic feature selection                   approach is to build up a subset of required number of features incrementally starting                   with the empty set (bottom-up approach) or to start with the complete set of features                   and remove redundant features until d features are retained (top-down approach). The                   simplest widely used choice, the  Sequential Forward (Whitney A. W., 1971) or                   Backward (Marill T., Green D., 1963), Selection methods – SFS (SBS) – iteratively add                   (remove) one feature at a time so as to maximize the intermediate criterion value until                   the required dimensionality is achieved. Earlier sequential methods suffered from the                   so-called “nesting” of feature subsets, which significantly deteriorated the                   performance. The first attempt to overcome this problem was to employ either the","Castek_1_Castek  23.1.2015  7:37  Stránka 49                                                                    3.4 SUB-OPTIMAL SEARCH METHODS  49                     Plus-l-Minus-r, also known as “(l,r)” or “+L-R” (Stearns S. D., 1976) which involves                   successive augmentation and depletion process, or generalized algorithms (Devijver                   P. A., Kittler J., 1982). Among later approaches the following two families of methods                   can be pointed out for general applicability and performance reasons: Sequential                   Forward (or Backward) Floating Search methods SFFS, SBFS (Pudil P., Novovičová J.,                   Kittler J., 1994), and Oscillating Search (OS) methods (Somol P., Pudil P., 2000). An                   overview of the evolution of sequential search methods is given in Table 3-1.                         Table 3-1: Evolution of sequential search methods                       Method (Simplest first)            Proper es / Improvement over previous method                                                       Evaluate each variable separately, completely                    Best Individual Features (BIF)                                                      ignore variable rela ons                                                      Sequen ally build subset, in each step with                    SFS / SBS (Sequen al Selec on)                                                      respect to the currently included features                                                      As SFS/SBS, but in each step evaluate groups of                    GSFS / GSBS                                                      features instead of single features to reveal more                    (Generalized Seq. Sel.)                                                      complicated dependencies                                                      Prevent “nes ng”: alternate the adding and                    Plus‐l‐Minus‐r                                                      removing of one feature based of parameters L                                                      and R                                                       Same as Plus‐l‐Minus‐r, but in each step evaluate                    GPlus‐l‐Minus‐r (Generalized P‐l‐M‐r)  groups of features instead of single features to                                                      reveal more complicated dependencies                                                      Automa cally determine the sequence of                    SFFS / SBFS (Floa ng Search)      addi ons and removals – to avoid user parameters                                                      and improve search effec veness                                                      As SFFS/SBSF, but in each step evaluate groups of                    GSFFS / GSBFS (Generalized Float. S.)  features instead of single features to reveal more                                                      complicated dependencies                                                      Automa cally adjust the size of feature groups                    ASFFS / ASBFS (Adap ve Float. Search)  evaluated in each step to be er focus on desired                                                      dimensionality                                                      Focus straight on the desired dimensionality +                    OS (Oscilla ng Search)            enable greater flexibility: op onal randomized                                                      search, result tuning,  me‐constrained search etc.","Castek_1_Castek  23.1.2015  7:37  Stránka 50                   50  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                     Floating search methods                     The Sequential Forward Floating Selection (SFFS) procedure consists of applying a                   number of backward steps (removing the feature, that causes the least criterion                   decrease) after each forward step (adding the feature that maximizes the criterion the                   most) as long as the resulting subsets are better than previously evaluated ones at that                   level (see Fig. 3-11). Consequently, there are no backward steps at all if the                   intermediate result at the actual level (of corresponding dimensionality) cannot be                   improved. The same applies for the backward version of the procedure. Both                   algorithms allow a “self-controlled backtracking” so they can eventually find good                   solutions by adjusting the trade-off between forward and backward steps dynamically.                   In a certain way, they compute only what they need without any parameter setting                   (unlike Plus-l-Minus-r).                    Figure 3-11: Sequential Forward Floating Selection Algorithm                                         A formal description of this now classical procedure can be found in Pudil P.,                   Novovičová J., Kittler J. (1994). Floating search algorithms have been critically                   acclaimed as universal tools not only outperforming all predecessors, but also keeping                   advantages not met by more sophisticated algorithms (e.g. Kudo M., Sklansky J., 2000).                   They find good solutions in all problem dimensions in one run and the overall search                   speed is high enough for most practical problems.                       Recent experiments show that the floating search principle overcomes the                   optimization performance vs. generalization trade-off problem exceptionally well (see                   the experiments below). The idea of the floating search was later extended in the                   adaptive floating search algorithms (Somol P., Pudil P., Novovičová J., Paclík P., 1999).                     Oscillating search method                    The Oscillating Search (OS) (Somol P., Pudil P., 2000), can be considered a “higher-                   level” procedure, that takes use of other feature selection methods as sub-procedures                   within the main course of search. The concept is highly flexible and enables","Castek_1_Castek  23.1.2015  7:37  Stránka 51                                                                    3.4 SUB-OPTIMAL SEARCH METHODS  51                     modifications for different purposes. Unlike other methods, the OS is based on                   repeated modification of the current subset X of d features. In this sense the OS is                                                           d                   independent from the pre-dominant search direction. This is achieved by alternating                   the so-called “down- and up-swings”. Both swings attempt to improve the current set                   X by replacing some of the features by better ones. The down-swing first removes the                    d                   worst feature(s), then adds the best ones back, while up-swing first adds, then removes                   them. Two successive opposite swings form an oscillation cycle. The OS can thus be                   looked upon as a controlled sequence of oscillation cycles of specified depth (number                   of features to be replaced in one swing). The course of the OS search is compared to                   SFFS and SFS in Fig. 3-12.                     Figure 3-12: Comparing the course of search (current subset size depending on time) in standard                   sequential search methods                                      Every OS algorithm requires some initial set of d features. The initial set may be                   obtained randomly or in any other way, e.g., using some of the traditional sequential                   selection procedures. Furthermore, almost any feature selection procedure can be                   used to accomplish the up- and down-swings. This makes the OS more a framework                   than a single procedure. The OS can thus be adjusted for an extremely fast search (low                   cycle depth limit, random initialization) in problems of high dimensionality or a very                   intensive search aimed at achieving the highest possible criterion values (high cycle                   depth limit, repeated runs from different random starting points to avoid local                   extremes, or other complex initialization). The OS can be used to tune solutions                   obtained elsewhere.                       As opposed to all sequential search procedures, OS does not waste time evaluating                   subsets of cardinalities too different from the target one. This “focus” improves the                   OS ability to find good solutions for subsets of given cardinality. The fastest                   improvement of the target subset may be expected in initial phases of the algorithm                   run. This behaviour is advantageous as it gives the option of stopping the search after                   a while without serious result-degrading consequences (OS is thus usable in real-time                   systems). Moreover, because the OS processes subsets of target cardinality from the                   very beginning, it may find solutions even in cases where standard sequential                   procedures fail due to numerical problems.","Castek_1_Castek  23.1.2015  7:37  Stránka 52                   52  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                     3.4.3 Non-sequential and alternative methods                     A broad range of alternative approaches to feature selection is available in addition to                   sequential search methods, often having properties targeted at particular problems.                   Other alternatives aim at making the best of existing methods (not necessarily FS                   methods only) by means of combinations. Many methods inherit both the search                   procedure and subset evaluation criteria in one indivisible unit.                       Randomized methods. Sub-optimal sequential methods are prone to getting stuck                   in local extremes. Randomizing may help overcome this problem. It may also help                   find solutions in a significantly shorter time, although this is not guaranteed. The                   optimization power of purely randomized procedures like genetic algorithms (Hussein                   F., Ward R., Kharma N., 2001; Mayer H. A., Somol P., Huber R., Pudil P., 2000), has                   been found slightly inferior to sequential methods. Extending sequential methods to                   include limited randomization may be a good compromise, as is the case with a                   repeatedly randomly initialized oscillating search (Somol P., Pudil P., 2000). A well-                   known procedure performing the search semi-randomly with an inherited evaluation                   criterion is the relief algorithm Kononenko I. (1994).                       Hybrid methods. The motivation to take the best from various approaches led to                   development of the so-called “hybrid methods”. These usually attempt to make use of                   the better properties of several existing methods while suppressing their drawbacks;                   the search then often consists of steps performed by means of various sub-methods.                   Attempts have been made to achieve Wrapper-like performance in Filter-like search                   time, etc. The idea of hybridization is studied in detail in Liu H., Yu L. (2005).                       Mixture-modelling based methods. Mixture-modelling approaches are suitable                   especially when the data is large and suspected to be multi-modal or otherwise                   complex in structure. Mixture modelling methods enable simultaneous construction                   of decision rules and feature selection (Novovičová J., Pudil P., Kittler J., 1996;                   Novovičová J., Pudil P., 1997; Pudil P., Novovičová J., (1998).                       Problem-specific methods. In many fields standard methods can be used only with                   difficulties or not at all, often due to extreme dimensionality and a small number of                   samples in the input data. This is the case in genetics (Alexe G., Alexe S., Hammer                   P.L., Vizvari B., 2006), or text categorization (Forman G., 2003), where the individually                   best feature selection is often the only applicable procedure. Defining highly                   specialized criteria suitable for the particular task compensates for the deficiency of                   the BIF search.                       Many other methods exist (in all senses of the term “FS Method”), among others                   the generalized versions of the ones listed above, various randomized methods,                   methods related to use of specific tools (FS for Support Vector Machines, FS for Neural                   Networks) etc. For an overview see, e.g., A. K. Jain, R. P. W. Duin, and J. Mao (2000),                   H. Liu, L. Yu, (2005).","Castek_1_Castek  23.1.2015  7:37  Stránka 53                                                                    3.4 SUB-OPTIMAL SEARCH METHODS  53                     3.4.4 Pitfalls of feature subset evaluation – experimental comparison                          of criterion functions                    As stated before, in certain types of tasks it is important to judge the importance of                   individual features. Although the importance of every feature may be evaluated in                   decision theory, in practice 1) we usually lack enough information about the real                   underlying probabilistic structures and 2) analytical evaluation may become                   computationally too expensive. Therefore, many alternative evaluation approaches                   were introduced. It is generally accepted that in order to obtain reasonable results, the                   particular feature evaluation criterion should relate to a particular classifier. From this                   point of view, we may expect at least slightly different behaviour of the same features                   with different classifiers. In fact, even more differences can be observed between                   feature evaluation made using wrappers and filters.                    Table 3-2: Single features in descending order, first best 7 then last worst 7, according to individual                   criterion values (i.e., “individual discriminative power”), 4-class, 38-dimensional Australian credit                   scoring data                                   37    29     31     19      6      28     20     …      14                    Bha acharyya                                 24    23     13     32      0      12                                 37    31     29     6       19     28     20     …      14                    Divergence                                 24    23     13     32      0      12                                 29    30     31     28      37     2      26     …      0                    G.Mahalanobis                                 25    17     13     24      35     12                                 29    6      19     10      25     20     18     …      12                    Patrick‐Fisher                                 13    32     0      1       37     36                    Gauss. cl. (10‐f.  6  10  35     25      29     19     2      …      34                    CV)          8     9      20     33      31     37                     1‐NN (10‐fold  29  30     31     28      19     16     26     …      35                    CV)          37    12     14     36      1      2                     SVM lin (10‐f.  29  3     16     18      14     31     4      …      20                    CV)          27    22     15     6       7      24                          In the example in Table 3-2 we demonstrate the differences between some                   standard criterion functions – both the probabilistic measures (filter setting:                   Bhattacharyya, Divergence, generalized Mahalanobis, Patrick-Fisher distances) and                   the classification accuracy (wrapper setting: Gaussian classifier, 1-Nearest Neighbour,                   Support Vector Machine with linear kernel, classification accuracy evaluated by means","Castek_1_Castek  23.1.2015  7:37  Stránka 54                   54  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                     of 10-fold cross-validation). We evaluated single features of the Australian credit scoring                   data using each of the criteria and ordered them descending according to the                   respective criterion values. In this way the more distinctive features should appear in                   the left part of the table, while the noisy and less important should appear in the right.                   The differences in feature ordering illustrate the importance and also the possible                   pitfalls of the choice of suitable criterion. Although some features are evaluated as                   good by most of the criteria (Salappa A., Doumpos M., Zopounidis C., 2007; Somol                   P., Baesens B., Pudil P.,Vanthienen, J., 2005) and some as bad (Jain A. K., Duin R. P.                   W., Mao J., 2000), with many others the results vary considerably and may show                   conflicting evidence Ferri F. J., Pudil P., Hatef M., Kittler J. (1994), Kononenko I.                   (1994). This is an undesired effect illustrating how difficult it may be to draw general                   conclusions about which features are generally best to select – it can also be taken as                   an argument in favour of using wrappers instead of filters, to identify features with                   more certainty with respect to the given decision rule.                       Following the examples above, it can be concluded that by employing classifier-                   independent criteria one accepts certain simplification and possibly misleading                   assumption about data (note that most of probabilistic criteria are defined for                   unimodal normal distributions only). Nevertheless, classifier-independent criteria                   may prove advantageous to prevent over-fitting in cases when wrapper based feature                   selection fails to identify feature subsets that generalize well.                     3.4.5 Summary of recent sub-optimal feature selection methods                    Our own research and experience has led us to the conclusion that no unique generally                   applicable approach exists to the feature selection problem. Some feature selection                   approaches and methods are more suitable under certain conditions; others are more                   appropriate under other conditions, depending on the properties and our knowledge                   of the given problem. Hence, continuing effort is invested in developing new methods                   to cover the majority of situations which can be encountered in practice.                       Recent developments in algorithms for optimal search have led to considerable                   improvements in the speed of search. Nevertheless, the exponential nature of optimal                   search remains and will remain one of the key factors motivating the development of                   principally faster sub-optimal strategies. Floating search and oscillating search methods                   deserve particular attention among the family of sequential search algorithms as a                   practically useful compromise between speed and optimization performance.                       We can give the following recommendations based on our current experience–                   the floating search can be considered the first tool to try, as it is reasonably fast and                   generally yields very good results in all dimensions at once, often succeeding in finding                   global optimum with respect to the chosen criterion. The floating search also shows                   to be a good compromise to deal with the optimization efficiency versus generalization                   (impact on classifier performance on unseen data) trade-off. The oscillating search                   may become a better choice when: 1) the highest possible criterion value must be","Castek_1_Castek  23.1.2015  7:37  Stránka 55                                                                    3.4 SUB-OPTIMAL SEARCH METHODS  55                     achieved but optimal methods are not applicable, 2) a reasonable solution needs to                   be found as quickly as possible, 3) numerical problems hinder the use of standard                   sequential methods, 4) extreme problem dimensionality prevents any use of standard                   sequential methods, or 5) the search is to be performed in real-time systems. The                   oscillating search shows an outstanding ability to avoid local extremes in favour of                   finding the global optimum, especially when repeated with different random initial                   feature subsets.                       It should be stressed that, as opposed to the optimal branch \& bound algorithm,                   the sub-optimal sequential methods are tolerant to deviations from monotonic                   behaviour of feature selection criteria. It makes them particularly useful in conjunction                   with non-monotonic FS criteria like the error rate of a classifier (cf. wrappers Kohavi                   R., John G.H., 1997), which according to a number of researchers seem to be the only                   legitimate criterion for feature subset evaluation. The superior performance of                   wrappers over filters has been verified experimentally (e.g. Pudil, Somol, 2008).                     3.4.6 Dependency-Aware Feature Selection (DAF)                    A relatively new member of the family of FS methods is the so-called “Dependency-                   Aware Feature Selection” (Somol P., Grim J., Pudil, P., 2011). Though it is not a                   “classical search method” but rather a ranking method, it can be used for feature                   selection too. Since the DAF method has been used in our research (as described in                   the following chapters) we shall describe it briefly in the following.                       Problems stemming from an insufficient sample size with respect to problem                   dimensionality are not typical only for a high-dimensional FS; such situations can                   appear even in low-to-mid-dimensional problems as is common in economics or                   medicine (Liu H., Yu L., 2005) for instance, where the number of observed cases is                   often too limited. In cases of an insufficient data sample size it may be questioned                   what information about the features can be reliably obtainable from the data at all                   (Pudil P., Novovičová J., Kittler J., 1994; Pudil P., Novovičová J., Kittler J., 1994; Raudys                   Š., 2006). The commonly suggested work-around is to refrain from complex analysis                   of feature subsets in favour of simpler FS methods or even trivial feature ranking, also                   known as the Best Individual Features (BIF) method (Ripley B., 1996; Salappa A.,                   Doumpos M., Zopounidis C., 2007). It is commonly assumed that ignoring inter-                   feature dependencies is less harmful than obtaining misleading information through                   serious estimation errors due to over-fitting.                       Assume a general pattern recognition problem (typically a classification or                   clustering problem) in an N-dimensional feature space. In the particular case of                   classification, some objects described by means of features f , f , … f (real valued or                                                                       1                                                                         2                                                                              N                   discrete) are to be classified into one of a finite number of mutually exclusive classes.                   The common initial step in classifier design is to choose a reasonably small subset of                   informative features by using a feature selection method.","Castek_1_Castek  23.1.2015  7:37  Stránka 56                   56  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                     Denoting F the set of all features                                                 F={f , f , … f }                                                     1 2                                                            N                   we assume that for each subset of features S ⊂ F a feature selection criterion J (•) can                   be used as a measure of quality of S (typically but not necessarily from the classification                   point of view). According to the standard FS paradigm, the resulting feature subset is                   obtained by maximizing J (S) over the class of all subsets S ⊂ F.                       Here we do not impose any restrictions on the function J (•) except that we expect                   it to be capable of reflecting feature behaviour in context, i.e., it should provide more                   than just combined information on individual feature merit.                                                                                       3                       A specific FS problem arises in case of very high dimensionality, e.g., N ≈10 ÷ 10 6                   or even more. Even the simplest sub-optimal optimization techniques are exceedingly                   time-consuming in such cases and, consequently, only very basic tools can be used to                   optimize features. The common approach is a simple ranking of features based on the                   individual feature quality (cf. BIF). By ordering the features according to the inequality                                                       }); n=2, 3, …, N                                           J({fi n-1 }) ≤ J({fi n                                                                                         but,                   we can easily identify a subset of d individually best features fi N-d+1   , fi N-d+2  , …,fi N                   in this way, we completely ignore the potentially crucial dependence among features                   and the resulting subset thus may be far from optimal.                       The DAF method attempts to generalize the idea of individually best ranking by                   evaluating the quality of each feature repeatedly in the context of randomly chosen                   feature subsets. In other words, we evaluate the quality J ({f } ∪ S) for a sufficient                                                                        n                   number of random subsets S ⊂ F, (f ∉ S) and compare the corresponding mean value                                                 n                   S with the analogous mean of J (S) for subsets S ⊂ F not containing the feature f ,                                                                                          n                   (i.e. f ∉ S).                       n                       This idea is based on the intuitive assumption that “good” features exhibit                   reasonably consistent behaviour in context with other features, that this information                   is obtainable easily enough and that it can improve upon the information about                   individual feature quality. An analogous mechanism has been shown to perform well                   in Fast Branch \& Bound algorithm (Somol P., Pudil P., Kittler J., 2004), where feature                   behaviour is studied in variable context and the averaged information is utilized to                   predict J (•) values, enabling considerable acceleration of the search process.                       The starting point of the proposed dependency-aware feature ranking is a                   randomly generated sequence of feature subsets, to be denoted probe subsets                                       S = {S , S ,..., S }, S ⊂ F, j = 1, 2,... , K,                                                        j                                            1                                               2                                                    K                   where each subset is evaluated by a criterion function J (•). The cardinality of the                   subsets S ∈ S should vary and the resulting sequence S should be long enough to                   “approximate” the class of all possible subsets of F in a reasonably uniform way. For                   each feature f ∈ F there should be enough subsets in S that do contain it as well as                   enough subsets that do not.","Castek_1_Castek  23.1.2015  7:37  Stránka 57                                                                    3.4 SUB-OPTIMAL SEARCH METHODS  57                         To generate a random probe subset we use the following simple procedure: first                   the subset size d is randomly chosen so that d ∈ [1, min{N, τ}] where τ ∈ [1,N] is an                   optional user-specified upper limit. Next, indexes of features to be selected are                   randomly generated from [1, N] as long as the number of unique feature indexes is                   lower than d.                        Given a sufficiently large sequence of feature subsets S, we are interested in                   utilizing the information contained in the criterion values J(S ), J(S ), ..., J(S ) in                                                                                        K                                                                                2                                                                           1                   depth. Instead of measuring the classification “power” of individual features f ∈ F, we                   compare the quality of probe subsets containing f with the quality of probe subsets                   not including f.                       A straightforward idea is to compute the mean quality μ of subsets  S ∈ S                                                                            f                   containing the considered feature f ∈ F                                         –                   and the mean quality μ of subsets S ∈ S not containing the considered feature f:                                       f                        with the aim of using the difference of both values as a criterion for ranking the                   features:                            Note that the “dependency aware” ranking criterion DAF does not measure the                                                                         0                   individual quality of a feature f ∈ F separately by means of the criterion value J(f), but                   takes into account the quality of feature f in the context of other features occurring in                   the sets S ∈ S. The value DAF (f) can be viewed as the average benefit of including                                             0                   the feature f into the feature subsets S ∈ S.                       To conclude, the DAF method ranks the features according to the average benefit                   of including a feature into a number of randomly generated feature subsets. The benefit                   is expressed as the difference of mean criterion values computed for subsets that do                   and do not contain the feature, based on arbitrarily chosen feature selection criterion.                   This simple idea has been shown quite suitable for high and very-high-dimensional                   feature selection problems where it is capable of considerably over-performing the                   commonly used individual feature ranking approaches due to its favourable mix of                   properties: the ability to reveal contextual information, reasonable speed, and                   generalization ability. Moreover, it has also been proven to have good properties with                   respect to the stability of solution, discussed in the following.","Castek_1_Castek  23.1.2015  7:37  Stránka 58                   58  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                     3.5 Performance Estimation Problem                      A comparison of FS methods needs to be performed with caution, paying attention                   to the further mentioned aspects of the problem. It is very different whether we                   compare concrete method properties or the final classifier performance determined                   by use of particular methods under particular settings. Researchers frequently break                   the basic requirement of using different data sets for training and testing. In such a                   case (denoted as  resubstitution), the results are biased and too optimistic. The                   performance on an independent data set (and thus the required ability of learning                   methods to generalize) is generally worse.                       Certainly, final classifier performance (on independent test data) is the ultimate                   quality measure. However, as stated in more detail in Section 6, misleading                   conclusions about FS may be easily drawn when evaluating nothing else, as classifier                   performance depends on many more different aspects then just the actual FS method                   used. Nevertheless, in the following we will adapt classifier accuracy as the main means                   of FS method assessment.                       There seems to be a general agreement in the literature that wrapper-based FS                   enables the creation of more accurate classifiers than filter-based FS. Nevertheless,                   this claim is to be taken with caution, while using actual classifier accuracy as the FS                   criterion in wrapper-based FS may lead to the very negative effects mentioned above                   (over-training). At the same time, the weaker relation of filter-based FS criterion                   functions to particular classifier accuracy may help better generalization. However,                   these effects can be hardly judged before the building of the classification system has                   actually been accomplished.                       We will focus only on wrapper-based FS in the following. Wrapper-based FS can                   be accomplished (and accordingly its effect can be evaluated) using one of the                   following methods:                   •   Re-substitution – In each step of the FS algorithm all data is used both for classifier                       training and testing. This has been shown to produce strongly optimistically                       biased results.                   •   Data split – In each step of the FS algorithm the same part of the data is used for                       classifier training and the other part for testing. This is the correct way of classifier                       performance estimation, yet it is often not feasible due to the insufficient size of                       available data or due to the inability to prevent bias caused by unevenly                       distributed data in the dataset (e.g., it may be difficult to ensure that with two-                       modal data distribution the training set will not represent one mode by                       coincidence and the testing set the other mode)                   •   Cross-Validation (CV) – Training data is split into several parts. Then in each FS                       step a series of tests is performed, with all but one data part used for classifier                       training and the remaining part used for testing. The average classifier                       performance is then considered to be the result of FS criterion evaluation. Because","Castek_1_Castek  23.1.2015  7:37  Stránka 59                                             3.6 PROBLEM OF FEATURE SELECTION OVERFITTING AND STABILITY  59                         a different part of data in each test is used for testing, all data is eventually utilized,                       without actually testing the classifier on the same data on which it had been                       trained. This is significantly better than re-substitution.                   •   Leave-one-out – A special case of CV with just one sample left for testing in each                       data split. This is computationally more expensive, but better utilizes the data.                   •   Hold-Out (HO) – Training data is randomly sampled. A series of tests is                       performed in each FS step, with a part of the training data randomly sampled for                       classifier training and another part randomly sampled for testing. The average                       classifier performance is then considered to be the result of a FS criterion                       evaluation. Unlike CV, this may avoid possible bias caused by deterministically                       and evenly split data, but possibly requires a higher number of trials than CV.                      3.6 Problem of Feature Selection Overfitting and Stability                     The prevailing approach to FS method performance assessment in older literature was                   to evaluate the ability to find the optimum, or to get as close to it as possible, with                   respect to some criterion function defined to distinguish classes in classification tasks                   or to fit data in approximation tasks. Recently, emphasis has been put on assessing the                   impact of FS on generalization performance, i.e., the ability of the devised decision                   rule to perform well on independent data. It has been shown that similarly to classifier                   over-training, the effect of feature over-selection can hinder the performance of a                   pattern recognition system (Raudys, 2006), especially with small-sample or high-                   dimensional problems. Compare Figures 3-13 and 3-14 to see an example of the effect.                       Figure 3-13 shows the maximal criterion value obtained by each method for each                   subset size. It can be seen that the strongest optimizer in most of the cases is OS,                   although SFFS falls behind just negligibly. SFS’s optimization ability is shown to be                   markedly lower, but still higher than that of BIF’s.                       Figure 3-14 shows how the optimized feature subsets perform on independent                   test data. From this perspective the differences between methods is largely diminished.                   The effects of feature over-selection (over-fitting) affect the strongest optimizer – OS                   – the most. SFFS seems to be the most reliable method in this respect. SFS yields the                   best independent performance in this example. Note that although the highest                   optimized criterion values have been achieved for subsets of roughly 6 features, the                   best independent performance can be observed for subsets of roughly 7 to 13 features.                   The example thus is effective in illustrating one of the key problems in FS – the                   difficulty to find subsets that generalize well, related to the problem of feature over-                   selection (Raudys, 2006).                       The speed of each method tested decreases with its complexity. BIF runs in linear                   time. Other methods run in polynomial time. SFFS runs roughly 10× slower than SFS.                   OS in the slow test setting runs roughly 10 to 100× slower than SFFS.","Castek_1_Castek  23.1.2015  7:37  Stránka 60                   60  3 FEATURE SELECTION METHODS IN STATISTICAL PATTERN RECOGNITION                     Figure 3-13: Sub-optimal FS methods’ optimization performance on 3-NN wrapper                                            Figure 3-14: Sub-optimal FS methods’ performance verified using 3-NN on independent data                                                   It has also been pointed out that independent test data performance should not                   be neglected when comparing FS methods (Reunanen, 2003). There seems to be a                   general agreement in literature that wrapper-based FS enables the creation of more                   accurate classifiers than filter-based FS. This claim is nevertheless to be taken with                   caution, while using actual classifier accuracy as FS criterion in wrapper-based FS                   may lead to the very negative effects mentioned above (overtraining). At the same                   time, the weaker relation of filter-based FS criterion functions to particular classifier","Castek_1_Castek  23.1.2015  7:37  Stránka 61                                                                                      3.7 SUMMARY  61                     accuracy may help better generalization. Yet these effects can be hardly judged before                   building the classification system has actually been accomplished. The problem of                   classifier performance estimation is by no means simple. Many estimation strategies                   are available, the suitability of which is problem dependent (re-substitution, data split,                   hold-out, cross-validation, leave-one-out, etc. – see the Section 5). For a detailed study                   on classifier training related problems and work-around methods, e.g., stabilizing                   weak classifiers, see Skurichina (2001).                     3.6.1 Problem of Feature Selection Stability                    As already stated before, it is common that classifier performance is considered the                   ultimate quality measure, even when assessing the FS process. However, misleading                   conclusions may be easily drawn when ignoring stability issues. Unstable FS                   performance may seriously deteriorate the properties of the final classifier by selecting                   the wrong features. Following Kalousis et al. (2007) we define the stability of the FS                   algorithm as the robustness of the feature preferences it produces to differences in                   training sets drawn from the same generating distribution. FS algorithms express the                   feature preferences in the form of a selected feature subset S ⊆ Y. Stability quantifies                   how different training sets drawn from the same generating distribution affect the                   feature preferences. Recent works in the area of FS methods’ stability mainly focus on                   various stability indices, introducing measures based on Hamming distance (Dunne                   et al., 2002), correlation coefficients and Tanimoto distance (Kalousis et al., 2007),                   consistency index (Kuncheva, 2007) and Shannon entropy (Křížek et al., 2007).                   Stability of FS procedures depends on the sample size, the criteria utilized to perform                   FS, and the complexity of FS procedure, Raudys (2006).                       Two new measures called consistency and weighted consistency, which express the                   stability or robustness of FS method with respect to various data samplings, have been                   introduced in Somol et al. (2008a).                       3.7 Summary                     We have shown in this chapter that a battery of dimensionality reduction methods                   exists within the context of statistical pattern recognition. We claim that many of these                   methods are directly (or with just minor adjustments) applicable to solving managerial                   problems. In particular the problem of identifying factors of competitiveness in                   companies can be considered a special case of the general feature selection problem                   known within statistical pattern recognition. Managerial problems of this type can be                   approached using feature selection tools to great advantage, following from the fact                   that such dimensionality reduction techniques are well established and understood.","Castek_1_Castek  23.1.2015  7:37  Stránka 62","Castek_1_Castek  23.1.2015  7:37  Stránka 63                                                                                                   63                             4 Testing approaches and methods based                      on learning methods for identifying factors                       of competitiveness                          4.1 Introduction                     The issue of searching for corporate competitiveness factors represents an attractive                   and very topical matter for both practice and theory and is discussed in more detail                   in the introductory chapter of this monograph. Summarising studies quote dozens of                   works (e.g. 82 studies in the meta-analysis by Allouche and Laroche, 2005) and                   bibliographic databases index thousands of articles annually on this topic. However,                   these works do not present a unified school of thought, as they differ in their                   approaches to the issue, terminology used, application of methods and reasons for                   dealing with the issue as well as the credibility of the results and the ways they are                   applied (Ambastha and Momaya, 2004).                       Within the context of corporate competitiveness factors, i.e. the causes that                   influence competitiveness substantially, we focus on one of the key issues – the synergy                   problem. This refers to the reality that a firm’s competitiveness is not the result of a                   partial effect of individual factors, but of their synergistic effect. This is often                   mentioned in the literature focused on mergers or inter-company and intra-company                   cooperation (Carter, 1977; Williamson and Verdin, 1992), while papers focused on                   other potential sources of competitive advantage view competitiveness as a                   multidimensional concept (Fraj-Andrés et al., 2008).                       The literature analysed implies that for the purposes of the search and evaluation                   of corporate competitiveness factors, there is quite a wide variety of different                   mathematical and statistical methods and techniques. First, we should mention                   bivariate techniques. From earlier studies, we can mention White (1986) and his study                   of the influence of generic strategies on return on investment and sales growth, where                   he used correlation, frequencies and averages. Further, we can cite Hansen and                   Wernerfelt (1989), who researched the influence of economic and organisational factors                   on ROA using correlations. As far as more recent studies are concerned, we should                   stress Artiach et al. (2010), who used correlations and t-tests to verify the influence of","Castek_1_Castek  23.1.2015  7:37  Stránka 64                   64  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     selected factors on the position of companies in the Dow Jones Sustainability Index,                   or Liu et al. (2004), who also used correlations. However, bivariate techniques cannot                   capture the complexity of reality nor the above-mentioned synergistic effect because                   they always analyse only the relationship between two variables.                       The authors believe that corporate competitiveness, even if narrowed down to                   Corporate Financial Performance (CFP in further), depends on many factors and that                   the influence of these factors needs to be examined as mutual associations between a                   number of interconnected variables and CFP. Our view is in accordance with empirical                   studies of corporate competitiveness using advanced statistical methods which range                   from multiple regression (Homburg et al., 1999; Cagwin, D., 2006), multiple logistic                   regression (Kessler, 2007) through structural modelling (Yilmaz et al., 2005), to decision                   trees (Molina et al., 2004). Unlike bivariate techniques, these procedures test the                   dependence of diversely measured performance or corporate competitiveness on                   multiple independent variables. This usually provides a better explanation of the                   variability in the performance of companies. However, their use requires certain                   restrictions, such as the normality of the input data or a robust a priori model. Thus,                   each of these methods has its limitations, requirements and drawbacks. Similarly,                   though the first results (cf. Blazek et al., 2008) of the Centre the Research Centre for                   Competitiveness of the Czech Economy (RCCCE) were based mainly on bivariate                   analysis of these variables, the fact that they are generally not mutually independent                   resulted in using methods of multivariate analysis. The authors aim to show that the                   methodology of feature selection in statistical pattern reduction, rarely used in this                   context in the past (cf. Pudil et al., 2002), is a well-developed methodology fulfilling                   this task.                       The fundamental problem to be solved is to analyse the characteristics of                   companies and to identify the factors on which their competitiveness depends. A large                   dataset is available for this purpose. As described in more detail in the following                   paragraphs, it consists of approximately 400 companies where each company is                   characterized by a relatively high-dimensional vector (it means in our case by some                   70 variables). Furthermore, each company is evaluated by one or several values that                   express its successfulness, assessed by means of expert knowledge. However, the data                   set is not complete. Some values are missing; moreover, different values are missing                   for different companies. Another very important characteristic of the data set is in the                   fact that it consists of different types of variables (features). Some of them are                   quantitative (numerical); some are ordinal or even categorical.                       There is no single and unique approach to the solution of this very complex                   problem since it depends on several options. The first choice is whether the problem                   should be looked upon as a classification or as a regression problem. These two types                   of problems can be solved by different sets of tools and the respective solutions have                   different properties.                       The input data contain one specific continuous value for each company, denoting                   a measure of its successfulness. Consequently, it offers the possibility of considering","Castek_1_Castek  23.1.2015  7:37  Stránka 65                                                                                  4.1 INTRODUCTION  65                     the problem at hand as a regression problem, while at the same time it is possible to                   transform the problem into a classification problem. This can be done simply by                   discretizing the value of successfulness (e.g. ROA in our case) into several values,                   which effectively means assigning the companies according to their value of                   successfulness into several classes (e.g. successful, neutral, unsuccessful). By                   transforming this into a classification problem, we lose some information and impose                   a potentially inexact division on the data, which increases the danger of achieving                   misleading results. However, on the other hand, the classification task may be solved                   more easily and thus the resulting classification rule may better describe the less                   precisely formulated problem. Therefore, the classification approach can perform a                   more successful “data-mining” when considering the whole problem. Obviously, it                   cannot be guaranteed in the case of very unfavourable properties of data (a small                   sample size, high dimensionality, a very complex distribution which cannot be                   assessed with a small sample in a sufficiently robust manner). In our case, we face                   these problems to a large extent as a preliminary analysis of the data set shown. The                   data we have at disposal are multimodal, strongly non-linear, incomplete and non-                   homogeneous.                       Apart from the issues of regression or classification there is another question –                   how to evaluate the dependence of the company quality (or successfulness) on the                   variables (features) characterizing companies. In principle, we could try to attain this                   information directly from the data without any modelling. However, this approach                   gives very limited options. As an example, it is possible to evaluate individual                   correlations of features with the successfulness of a company. The introductory                   analyses have shown that such an analysis did not lead to the goal. No single features                   that could describe the successfulness of companies sufficiently well were found. As                   expected, these attempts have shown that it is necessary to utilise multi-dimensional                   feature subspaces in order to reveal at least some reasonable link between the features                   and successfulness. To make it more illustrative, we can use as an example the two                   following figures.                       It can be seen that although we can have two features where each of them has a                   very low discriminative power (therefore very low informativeness I (F1), I (F2)) when                   considered separately (or isolated), by considering them both as a pair, the                   informativeness can substantially increase and even be several times higher than the                   sum of individual measures of informativeness.                       Based on all these reasons, it is instead a more reasonable “intrinsic analysis” to                   approach the data analysis by means of modelling as described in the following. The                   usage of model presents the possibility of gaining some knowledge on data                   distribution, to a certain extent including the subspaces with few or no samples.                   It also makes it possible to generalize, e.g. in prediction context. By modelling                   we understand creating a simplified formal description of data which substantially                   simplifies further analyses and makes it possible to find out generalizing                   information.","Castek_1_Castek  23.1.2015  7:37  Stránka 66                   66  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     Figure 4-15a: Informativeness of isolated features                                              Figure 4-15b: Synergic effect of more features                                                     In order to verify the above-specified hypothesis, two approaches have been                   investigated, differing in the way the factors group is selected and how the CFP is                   defined:                   1.  “Pattern classification approach” – by means of the informativeness for                       classification into a pre-defined set of mutually exclusive classes of companies;","Castek_1_Castek  23.1.2015  7:37  Stránka 67                                     4.2 FEATURE SELECTION BASED EVALUATION OF COMPETITIVENESS FACTORS  67                     2.  “Regression approach” - by means of the non-linear regression model accuracy.                       The first approach was the primary focus of our paper at the 8th European                   Conference on Management Leadership and Governance (cf. Pudil et al., 2012). The                   second approach was presented (for different datasets) in our papers at the 1st and                   the 2nd International Conference on Management Leadership and Governance (cf.                   Pudil et al., 2013; Somol et al., 2014).                       For the purpose of classification, (cf. Pudil et al., 2012) companies were grouped                   into three classes on the two-indicator space. The companies with an above average                   value of the CFP coefficient were denoted as having a good CFP, thus “successful”                   (group A, included 165 companies). On the other hand, the companies having a                   negative assets growth or/and with a negative ROA were denoted as “unsuccessful”                   (group C, included 82 companies). The remaining companies became the                   “intermediate” group B.                       For the regression analysis, we do not need the class information but a single                   continuous value expressing the overall CFP. For this purpose, we used the sum of                   Assets Growth and Return on Assets (more in chapter 2).                       4.2 Feature selection based evaluation of competitiveness                        factors                      As stated above, the multivariate analysis has to be used for the investigated task. In                   the context of machine learning, however, multivariate analysis is common and the                   available analysis frameworks have been considered vital in various recognition tasks                   (credibility scoring, image analysis, automated medical diagnostics /cf. Theodoridis                   and Koutroumbas, 2006/). One of the key approaches to multi-variate analysis is                   feature selection (FS), described in more detail in the previous chapter.                       The problem we face here is selecting a smaller subset of the most informative                   characteristics from the set of all the characteristics measured (variables, features).                   The informativeness is measured here by the ability of a subset to correctly                   discriminate classes according to their financial performance (groups A, B and C).                   Selecting a smaller subset of characteristics means effectively performing a                   dimensionality reduction on the original data. As stated in the previous chapter, the                   principal goal of FS is to select a small subset of variables with the aim of                   discriminating among classes of observations. We used FS methodology to search for                   a subset of characteristics which discriminate between the group of A companies and                   the group of C companies as much as possible. The idea about using the statistical                   pattern recognition approach for specifying competitiveness factors is based on the                   analogy of both the problems:","Castek_1_Castek  23.1.2015  7:37  Stránka 68                   68  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     Table 4-3: Analogy of problems of statistical pattern recognition and the problem of determining                   competitiveness factors                           Sta s cal pa ern recogni on        Determining compe  veness factors                      –“pa ern” is described by a real  D‐  –all companies are represented by D indices                                                           (characteris cs, variables, features)                       dimensional vector y = (y , y , …y )  –they are classified into one from several                                           2                                               D                                         1                     –pa ern is to be classified into one from a  classes (in our case two or three classes)                       final number of different classes                                                          –the classifica on task is not the goal here;                     –it is a classifica on task combined with the                                                           however, the dimensionality reduc on helps                       reduc on of dimensionality of feature                                                           to iden fy “key factors” of compe  veness                       vectors on which the classifica on is based                                                          –feature selec on methods enable selec ng a                     –feature selec on methods enable selec ng a  reduced subset of characteris cs (features,                       reduced subset of features, op mal with                                                           op mal with respect to the discrimina ve                       respect to the discrimina ve ability (and the                                                           ability related to their compe  veness)                       following classifica on of other pa erns)                                                          –only the first stage is used in our problem                     –complete pa er recogni on task consists of                                                          –there is no need to determine a classifica on                       two main stages:                    rule                         – 1/ feature selec on                                                              – we use it only as an FS criterion                         – 2/ pa ern classifica on                   4.2.1 Feature Selection Methodology                   The methodology of feature selection, or more generally dimensionality reduction in                   machine learning, is very extensive and has been briefly described in the previous                   chapter. We utilize FS methodology in two ways:                   1/ to search for a subset of characteristics which best discriminate between                       companies of groups A, B and C as much as possible;                   2/ to search for a subset of characteristics that minimizes the regression error.                       It should be noted that the resulting optimized subsets of these two different tasks                   might be different.                       The main advantage of non-trivial FS methods is their ability to evaluate                   characteristics in context, possibly extracting more information than is customary                   with commonly used ranking methods. In machine learning it is well known that “the                   two individually best features may not be the best pair”. Very often either the two                   individually best might prove redundant (each of them provides almost exactly the                   same information despite their seemingly different nature), or none of the features                   proves sufficient to reveal the true structure in the data (see Figure 4-16 for an                   illustration of a two-dimensional case; note that the same effects can take place in                   multiple-dimensional subspaces).                       As already stated in the previous chapter, in order to find the most informative                   subset of features, we need:                   –   an efficient strategy for traversing the space of possible subsets towards the                       optimum","Castek_1_Castek  23.1.2015  7:37  Stránka 69                                     4.2 FEATURE SELECTION BASED EVALUATION OF COMPETITIVENESS FACTORS  69                     –   a criterion of evaluating the quality of arbitrary subsets of features.                       A wealth of search strategies and criteria exists. There is no single strategy, nor a                   single criterion function known to be best in all cases. Moreover, our data had the                   limitation of a relatively high dimensionality and a low sample size which is rather                   typical in this type of analyses – the more characteristics we try to collect, the less                   companies we have available. With respect to this fact, we decided to first apply two                   conceptually different FS methods and to evaluate their performance not only in terms                   of results achieved, but also in terms of their stability (cf. Somol and Novovovicova,                   2010). Further analysis (Section 4.3.) will then be performed using the more stable                   (robust) method identified in the following Section 4.2.2.                    Figure 4-16: Cases of possible univariate analysis failure (illustrative example). Let the dots represent                   the companies of poor CFP and the rectangles represent the well performing companies. Univariate                   analysis is not capable of revealing a) competitiveness factor redundancy, b) multi-variate factor                   dependency leading to crucial model accuracy improvement in higher than one-dimensional                   subspace.                                            4.2.2 Evaluating Stability of Feature Selection Methods                    To evaluate candidate feature subsets in the stability test, we estimated the accuracy                   of the well-known k-Nearest Neighbour classifier (cf. Theodoridis and Koutroumbas,                   2006)). The advantage here is the simplicity, non-linearity (high descriptive power),                   adjustability of sensitivity to outliers through the k value, and most importantly, the                   possibility to redefine k-NN to support a mix of feature types: numerical and nominal.                   This was achieved by normalizing all numerical feature values to <0,1>, and defining                   the distance between nominal values as 0 in case of equality and 1 otherwise.                       As a search strategy, we chose a) Sequential Forward Floating Search (SFFS) (cf.                   Pudil et al., 1994), generally known for its good optimization performance but also","Castek_1_Castek  23.1.2015  7:37  Stránka 70                   70  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     good search speed, and b) Dependency-Aware Feature Ranking (DAF) (cf. Somol et                   al., 2011) known to be very robust against over-fitting.                       To compare the stability of results yielded by the two chosen FS methods, we                   repeated each experiment for each of the methods 20x, each time using a different                   randomly chosen 80% part of the available data. In each run, a subset of features was                   selected, possibly different from those of the other runs. The similarity of the various                   results is evaluated using various stability measures. Here we evaluate ANHI, ATI and                   CWr, (for an explanation and details cf. Somol and Novovovicova, 2010) in order to                   get a broader picture (no single measure is able to capture all aspects of the result                   observed). The goal is to possibly reveal the principal differences between the two FS                   methods employed with respect to solving our particular FS problem. The graphs in                   Figure 4-17 summarize the findings. It can be clearly seen that the stability of SFFS is                   considerably worse than that of DAF, regardless of the size of subset found and the k                   parameter of the employed FS criterion. Especially the low CWr values in case of SFFS                   suggest that SFFS tends to over-fit too much.                    Figure 4-17: Comparing SFFS and DAF stability and performance when selecting 5 or 15 features                   out of 37, with k-NN for k=1, 2, 3. Diamonds show k-NN accuracy achieved; other lines show stability                                       Based on the aforementioned observation, we decided to select features using the                   DAF method. The goal of this second experiment is to identify which features are                   better than the others, possibly yielding information about how much better they are.                   The criterion is again the estimated accuracy of k-NN classifier, now for k=5 as higher                   k values proved better to further prevent over-fitting (cf. Theodoridis, Koutroumbas,                   2006).","Castek_1_Castek  23.1.2015  7:37  Stránka 71                                          4.3 INTRODUCING THE MODIFIED FEATURE SELECTION METHODOLOGY  71                     4.3 Introducing the modified feature selection methodology                     In order to perform a feature selection process (analysis of the dependency between                   particular competitiveness factors and overall CFP over the available training data)                   using the chosen feature selection method in our particular case, we first need to                   impose a suitable model on the data that would describe the underlying data structure                   as accurately as possible. A good model can then be used to evaluate the quality of                   candidate subsets of characteristics in the process of feature selection. In the following,                   we consider two principally different approaches – classification and regression. The                   difference is in the measure of accuracy to be optimized. In the case of classification,                   we aim to identify such a subset of competitiveness factors, for which the model proves                   most accurate in distinguishing among the company groups A, B, and C (cf. Section                   4.4). In the case of regression, we avoid the grouping and aim to minimize the                   prediction error of a dependent variable expressing the overall CFP.                    Non-Parametric Model                    From the vast battery of existing models (cf. Theodoridis and Koutroumbas, 2006) our                   choices are limited due to two specifics of our problem: the data is incomplete (roughly                   5% of values are missing for various companies and various characteristics) and some                   of the available characteristics are non-numeric, i.e., their values are impossible to order.                   Another concern is the sample-size vs. dimensionality ratio, which in this case prevents                   application of models requiring large numbers of samples (mixture models or other                   multi-dimensional models, cf. Theodoridis and Koutroumbas, 2006, where the curse                   of dimensionality would quickly lead to over-training).                       As reported in (Pudil et al., 2012), a suitable approach is the application of k-                   Nearest Neighbor idea (Cover, Hart, 1967). k-NN is the non-parametric classifier that                   imposes a non-linear model taking direct use of existing samples in the training data                   set. Its known disadvantage – the necessity to permanently store the complete data                   set – is not a disadvantage in our case due to the limited data size and off-line nature                   of our search process. On the other hand its advantage – a good model fit and accuracy                   in the case of a limited data size – makes it a good choice for our purpose. The only                   additional tool needed is a suitably defined distance function capable of expressing                   the distance between any two samples (companies) in the 36-dimensional space of                   our data set. The commonly used distance is the Euclidean distance. A modification                   of standard Euclidean distance is the basis of how we handle missing values and non-                   numeric values.                     Handling Missing Values and Non-Numeric Values                    The accuracy of the model is affected not only by its fundamental principle but also                   by its possible parameters or other setup details. In our case, the handling of missing","Castek_1_Castek  23.1.2015  7:37  Stránka 72                   72  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     values and non-numeric values proves important. Both of these concerns are reflected                   in the definition of distance function used within the applied models.                       We considered two approaches of missing value handling, as expressed by the                   definition of pseudo-Euclidean distance:                   –   “standard” one-time substitution of each unknown value by the mean value over                       all known values for the respective feature in case of numeric features, or                       substitution by the most frequent value in case of non-numeric values                   –   “pessimistic” handling of unknown values when computing distance; missing                       values are always interpreted as if the distance was maximum with respect to the                       respective feature.                      4.4 Pattern classification approach                     In the classification approach, the DAF feature selection method (cf. Chapter 2) is                   applied to maximize the estimated prediction accuracy of the k-NN classifier. In the                   course of the search, the DAF method generates candidate feature subsets, evaluates                   each of them and collects the results to obtain a final feature ranking. Each candidate                   subset is evaluated as follows. The k-NN classifier is used to classify each single known                   company to one of the groups A, B, C purely based on the characteristics in the current                   subset. The result of classification is in each case compared to the known assignment                   of the respective company to one of the classes. Eventually, the percentage of                   companies classified correctly (predicted to belong to the same group where they                   actually belong) is used as the measure of subset quality.                     4.5 Regression approach and pseudo-kernel regression                        model                     Considering the CFP as the dependent variable, we tried to predict this dependent                   value by means of a special non-linear regression model with other company                   characteristics such as independent variables. The error of the regression model with                   given independent variables (companies characteristics) as regressors, thus the                   prediction error, serves in our approach as a criterion of how good these independent                   variables are for approximating the real CFP of companies in the data set. Such a                   subset of characteristics (features in pattern classification terminology, regressors in                   mathematical statistics terminology) that provides the lowest regression error can be                   then regarded as the set of key factors of corporate competitiveness.                       The only additional tool needed is a suitably defined distance function capable                   of expressing the distance between any two samples (companies) in the 37-                   dimensional (or 74-dimensonal) space of our data set. The commonly used distance","Castek_1_Castek  23.1.2015  7:37  Stránka 73                                         4.5 REGRESSION APPROACH AND PSEUDO-KERNEL REGRESSION MODEL  73                     is the Euclidean distance. A modification of standard Euclidean distance is the basis                   of our handling of missing values and non-numeric values.                       Applying regression instead of classification, as used in Pudil et al. (2012), has                   the potential benefit of preventing the impact of possible inaccuracies introduced                   when pre-processing data (at the moment of initial assignment of companies to                   classes). The regression model we have used is based on the “Kernel” regressor, where                   the dependent value is predicted as a linear combination over dependent values of                   existing samples, where more distant samples get a lower weight. “Kernel” in this                   context is the weighing function dependent on the distance among the point in                   question and existing samples (companies).                       More exactly, the proposed pseudo-kernel regression model is analogous to Parzen                   kernel models with Gaussian kernels with the main difference being in the fact that                   we assume only one-dimensional kernels. The unknown dependent value  y is                                                                                          k                   predicted as the weighted average of dependent variables of known companies. The                   one-dimensional Gaussian kernel in our case serves as the weight in the definition of                   distance between two companies,  w(x ,  x ). The Gaussian kernel thus helps to                                                       i                                                          j                   progressively reduce the influence of more distant companies and emphasizes the                   importance of close companies when predicting the dependent variable y for k-th                                                                                    k                   company. The pseudo-kernel regression model predicts the unknown competitiveness                   value y from neighbouring competitiveness values as follows:                         k                       The weighted distance between two companies is computed as follows:                         where L denotes the L -distance defined as:                          p                                       p                         Unless stated otherwise, we assume p=2, i.e., we primarily use the Euclidean distance.                   Note that σ is estimated from the training set as the standard deviation of pairwise                   distances of all known companies. The parameter  m is to be user-specified, or                   optimized in the pre-processing stage. Note that a higher value of m leads to a more                   smoothed-out model; a too high m would lead to a collapse of the model, which would                   then always predict the same average value of competitiveness. A lower value of m                   leads to a more detailed model that generalizes less. A too low m would collapse the","Castek_1_Castek  23.1.2015  7:37  Stránka 74                   74  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     model to an analogy of 1-Nearest Neighbour. Let us mention that both the m and p                   parameters can be optimized to minimize the model prediction error (see Section                   4.5).                       Note that the above formulation of pseudo-kernel regression model is still based                   on the assumption of companies being represented by numerical vectors without                   missing values. The resolution of this problem consists in redefining the L distance.                                                                                    p                   The problem of categorical variables can be diminished by assuming all numerical                   values to be normalized to [0,1]. In case of categorical variables, the contribution of a                   variable to the overall distance would then easily be 0 in case of equality or 1 in case                   of inequality of variable’s values. The problem of missing values can then be resolved                   by restricting the computation of L to only such a subspace on which all values are                                                  p                   known (provided the result is properly weighted). The other option is to interpret the                   missing value in one of two ways: either to indicate pessimistically that the distance                   is 1 (maximal), or to use the average distance computed over all cases where the                   variable is not missing.                       To explain it less mathematically – we gradually explore increasing subsets of                   features (companies’ characteristics) and use them as regressors for a special regression                   model. For a given subset of features, CFP for each company (serving as the dependent                   variable) is predicted by means of our regression model (see Figure 4-18). Now, let us                   consider a particular company. When trying to predict its CFP, we calculate it as a                   weighted sum of all the CFP’s of respective companies. The weight reflects the distance                   of the point representing our particular company from the point representing the                   respective company.                       To summarize the explanation presented above, we consider two regression                   models following an analogous idea as discussed in Sect. 4.3:                   1.  1-NN, where the dependent value for any point in the 36-dimensional space is                       predicted to be equal to that of such an existing sample that is the nearest to the                       point in question.                   2.  “Kernel” regressor, where the dependent value is predicted as a linear                       combination over dependent values of existing samples, where more distant                       samples get a lower weight. This model enables prediction based solely on the                       information about the distance between points in space; no coordinate                       information is used. This facilitates the definition of custom distance functions                       to accommodate features of various, even non-numeric types. The principle of                       the model is illustrated in Figure 4-18.                         This model has been shown capable of achieving a prediction error lower than                   3% in the paper by Pudil et al. (2013), despite the difficult modelled data set.                       The idea of “kernel” regression can be viewed as analogous to the idea of k-NN                   classifier (cf. Sect. 3.3.1). Similar to k-NN, our kernel regressor imposes a non-                   parametric non-linear model that directly uses information from the available data.                   When compared to the original kernel regression idea (cf. Nadaraya, 1964; Simonoff,","Castek_1_Castek  23.1.2015  7:37  Stránka 75                                                                        4.6 EXPERIMENTS AND RESULTS  75                     Figure 4-18: Given existing samples S , .., S and distance function d(), the yn value of sample Sn is                                                   3                                               1                   predicted as sum over w * y for i=1, .., 3, where wi reflects d(S ,S ) distance from 1-D Gaussian                                                                    n i                                      i                                         i                   kernel centered in S i                                 1996) we apply a slight modification. In order to accommodate the solutions to                   problems described in Sect 3.3.2, we apply only 1-dimensional Gaussian kernels on                   the space of sample distances. Kernel width is then optimized, starting initially from                   the estimated average distance between any two samples in the available data.                       In the regression approach, the DAF feature selection method (cf. Chapter 3, Sect.                   4.6) is applied to minimize the estimated error of predicted dependent values for each                   known company. The feature selection procedure is analogous to that described in                   Section 3.4.                      4.6 Experiments and results                     We primarily considered four different regression models in our key experiments,                   obtained by combining two types of regression models (1-Nearest Neighbour and                   Kernel Regressor) and two types of missing value substitution (substitution by mean                   value, and pessimistic treatment of each missing value as an indicator of maximum                   distance). Feature ranking by DAF (Somol et al., 2011) has been computed in each of                   the four cases so as to minimize the average model error. The DAF method produced                   a weight for each feature, mirroring roughly the average feature ability to improve the                   criterion value on addition to a subset, evaluated over a large number and variety of                   contexts (various subsets). Additionally, we performed classification-based                   experiments for comparison purposes.                     4.6.1 Regression-based analysis results                    The best-achieved models of the four types as described in Section 3.5 are illustrated                   in Figure 4-19.","Castek_1_Castek  23.1.2015  7:37  Stránka 76                   76  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     Figure 4-19: Errors of four regression models – each dot represents a company, positioned according                   to its Assets Growth (GA) and Return on Assets (ROA) values, a higher dot diameter depicts a higher                   regression error; black and grey colours depict its positive or negative value, respectively: a) 1-Nearest                   Neighbour with missing values substituted by mean values, b) Kernel Regressor with missing values                   substituted by mean values, c) 1-Nearest Neighbour with missing values treated pessimistically, d)                   (best) Kernel Regressor with missing values treated pessimistically.                                                                       The single best model identified in our survey – Kernel Regressor with pessimistic                   missing value substitution – achieved the average error of e= 0.0268903and determination                   coefficient Dc= 0.781963. The fact that a 1-dimensional kernel instead of a 36-dimensional                   kernel is used proved advantageous as it prevented over-fitting issues. Kernel regression                   thus proved more accurate in our experiments than simple 1-NN regression.                       The highest accuracy was achieved with the set of all features. Removal of any                   feature led to a degradation of results. The result of feature ranking is thus of interest","Castek_1_Castek  23.1.2015  7:37  Stránka 77                                                                        4.6 EXPERIMENTS AND RESULTS  77                     to compare the importance of various company characteristics though it has not lead                   to any decrease of dimensionality.                       The DAF method (cf. Somol et al., 2011) produced for each feature a weight,                   mirroring roughly the average feature ability to improve the criterion value on                   addition to a subset, evaluated over a large number and variety of contexts (various                   subsets). Figure 4-20 shows the weights obtained in the regression case, ordered in                   descending order. Note that the DAF weights obtained provide only the information                   about the relative quality of features when compared to other features. It can be seen                   that there are roughly up to 8 features that tend to improve criterion value considerably                   more than the others.                    Figure 4-20: Importance of single company characteristics according to the best-achieved regression                   model. The graph represents growing subsets of features, features added according to the highest                   DAF1 coefficients. Note that model accuracy markedly improves after adding the first 8 features,                   and then after adding roughly the next 7 features.                                               The best 8 factors (regression based) in decreasing order:                   Region                   –   DAF1 coefficient 1.11868, regressor error on single feature not computable due                       to missing values)                   Ratio of Technical and Administrative Staff                   –   DAF1 coefficient 1.10539, regressor error on 2 best features 0.104015                   Strategy                   –   DAF1 coefficient 0.782508, regressor error on 3 best features 0.101098                   Legal Form (legal form of the company)                   –   DAF1 coefficient 0.710418, regressor error on 4 best features 0.0983053                   Ownership Type (5 types of ownership)                   –   DAF1 coefficient 0.652801, regressor error on 5 best features 0.0920556","Castek_1_Castek  23.1.2015  7:37  Stránka 78                   78  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     FDI (domestic owner, foreign, both)                   –   DAF1 coefficient 0.483909, regressor error on 6 best features 0.085747                   Ration of Exports                   –   DAF1 coefficient 0.462479, regressor error on 7 best features 0.0698314                   Owners in Top Management (yes/no)                   –   DAF1 coefficient 0.408192, regressor error on 8 best features 0.0653676                        Regarded as factors of competitiveness within the framework of this pilot study,                   5 out of 8 these features (denoted in italics) correspond with the previous results of                   Spalek and Castek (2010) based on different analyses of similar data.                     4.6.2 Classification-based analysis results                    We performed a series of k-NN classifier based experiments for the values of k=1, 2,                   3, 5, and two types of missing value substitution (substitution by mean value,                   and pessimistic treatment of each missing value as an indicator of maximum                   distance).                       The single best classifier identified in our survey – 1-NN classifier with pessimistic                   missing value substitution – achieved the estimated classification accuracy of 0.873737                   for the subset of 32 features out of the complete set of 36. With the complete set, the                   accuracy is 0.866162. However, as illustrated in Figure 4-21, roughly half of all features                   are enough to achieve classification accuracy, only negligibly worse than the best                   achieved. k-NN classifiers for k>1 tend to smooth out the decision boundary, i.e.,                   reduce the influence of outliers at the cost of reducing sensitivity to detail. This effect                   proved disadvantageous in our case.                       The DAF method (cf. Somol et al., 2011) produced for each feature a weight,                   mirroring roughly the average feature ability to improve criterion value on addition                   to a subset, evaluated over a large number and variety of contexts (various subsets).                   Figure 4-21 shows the weights in classification case, ordered in descending order; note                   that the DAF weights provide only information about the relative quality of features                   when compared to other features. It can be seen that there are roughly up to 8 features                   that tend to improve the criterion value considerably more than the others.                        The best 8 factors (classification based) in decreasing order:                   Ratio of Technical and Administrative Staff                   –   DAF1 coefficient 1.1404, 1-NN accuracy on the single feature 0.472222                   Legal Form (legal form of the company)                   –   DAF1 coefficient 0.574625, 1-NN accuracy on best 2 features 0.472222                   ISO 14000-certificate holding (yes/no)                   –   DAF1 coefficient 0.42274, 1-NN accuracy on best 3 features 0.472222                   Assets Level                   –   DAF1 coefficient 0.284363, 1-NN accuracy on best 4 features 0.494949","Castek_1_Castek  23.1.2015  7:37  Stránka 79                                                                        4.6 EXPERIMENTS AND RESULTS  79                     Figure 4-21: Importance of single company characteristics according to best-achieved classification                   using 1-NN classifier and 3-class data. The graph represents growing subsets of features, features                   added according to highest DAF1 coefficients. Note that model accuracy markedly improves after                   adding the first 8 features, and then after adding roughly the next 10 features.                                         Owners in Top Management (yes/no)                   –   DAF1 coefficient 0.242903, 1-NN accuracy on best 5 features 0.494949                   Software Applications – SCM module (yes/no)                   –   DAF1 coefficient 0.206311, 1-NN accuracy on best 6 features 0.525253                   Ethical Code Adoption (yes/no)                   –   DAF1 coefficient 0.177655, 1-NN accuracy on best 7 features 0.563131                   Share of Performance-Related Pay                   –   DAF1 coefficient 0.164487, 1-NN accuracy on best 8 features 0.739899                         Regarded as factors of competitiveness within the framework of this pilot study,                   4 out of 8 these features (denoted in italics) correspond with the previous results of                   Spalek and Castek (2010) based on different analyses of similar data.                     4.7 Comparing Regression-based and Classification-based                        analysis results                     When comparing the results achieved by both the approaches discussed, we should                   bear in mind that our goal is not prediction but identification of “informative” factors.                   Thus, the error in predicting the CFP or in classifying a company is not critically                   important; what matters more is which factors are assigned to the group of key factors                   influencing the CFP and thus corporate competitiveness. In this context, we should                   not be too surprised that the regression approach and the classification one yield                   somewhat different results. We should keep in mind that the tasks solved by the","Castek_1_Castek  23.1.2015  7:37  Stránka 80                   80  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     respective approaches are not absolutely the same. The way of defining the CFP,                   implicitly hidden in these tasks, is different. In the regression approach, the CFP is                   defined by a combination of GA and ROA and attains continuous values. On the other                   hand, in the classification approach, the CFP is discretized by means of clustering the                   companies into distinct classes.                       Clearly, the classification approach does not utilize “fine” information about the                   value of CFP as the regression one does. On the other hand, as a generally accepted                   unique definition of CFP does not exist, clustering its values into distinct classes can                   also be a reasonable solution. This clustering certainly represents a simplification,                   representing a certain loss of information but at the same time having the potential                   benefit of giving more comprehensible information to the observer: the financial                   performance of a given company (and thus its competitiveness) is a good, average or                   bad one.                       In any case, by comparing these different approaches and analysing the results,                   we can get a more robust insight into the task.                     4.8 Improved Model for Attribute Selection                        on High-Dimensional Economic Data                     This section presents a newly improved procedure for estimating the model                   parameters, allowing us to achieve a significantly higher precision in feature subspaces.                   In other words, it improves the results when searching for a small set of factors of                   competitiveness. The performance of this improved procedure is illustrated in                   experiments with both the old multidimensional data (D=37) used in previous                   experiments, and with new data of higher dimensionality (D=74), which enabled us                   to reveal a not previously considered fact related to the estimates of the multiplication                   constant of the pseudo-kernel model.                     4.8.1 Improvements of the regression model                    Theoretical considerations verified in the course of experiments proved that the                   prediction accuracy of the pseudo-kernel non-linear regression model employed can                   be improved under certain conditions. These improvements are in possible                   adjustments to the distance function used and in optimizing the kernel width. They                   will be discussed in the following.                     Varying the distance function                    In the paper by Pudil et al. (2013), we assumed the standard L (Euclidean) distance                                                                         2                   to be used when evaluating distances between samples. Let us recall that for k =1, 2,                   … the higher order distance in D-dimensional space is defined as","Castek_1_Castek  23.1.2015  7:37  Stránka 81                         4.8 IMPROVED MODEL FOR ATTRIBUTE SELECTION ON HIGH-DIMENSIONAL ECONOMIC DATA  81                             In Figure 4-22 we illustrate that for the specific problem of corporate                   competitiveness, the L distance data is not necessarily the best option.                                       2                   Figure 4-22: Comparing Euclidean distance to alternative distances. Higher-order distance functions                   improve the accuracy of the kernel-based regression model on subspaces roughly of up to D/2 where                   D is the total number of features                                             Figure 4-23: Comparing accuracy of a pseudo-kernel regression model with a globally optimized                   multiplication constant m to a model with a locally optimized m.                   Note that a local optimization of m (optimization on subspace instead on full space) improves                   accuracy when a small number of features is used","Castek_1_Castek  23.1.2015  7:37  Stránka 82                   82  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                         Note that higher-order distances of up to L proved capable of improving the                                                              7                   model accuracy when a small number of features is used. We could not improve the                   best-achieved prediction accuracy, which remains roughly the same when all 74                   features are used. However, if the number of features considered is restricted to 25,                   the improvement in accuracy is clearly visible.                       The impacts of varying the distance function are presented in the following Table                   4-4. The “DAF” columns contain the values of DAF coefficients of corresponding                   features where these features are ordered in the decreasing order of their DAF                    Table 4-4: Comparing feature orderings yielded by model using Euclidean distance and L distance                                                                                     7                       74‐dimensional data, Euclidean distance  74‐dimensional data, L distance                                                                               7                                                Error on                             Error on                       DAF         Feature                 DAF          Feature                                                 subset                              subset                    0.00378051 Span of Control  0.0884389  0.00869157 Strategy      0.0885776                                                                   Mo va on of                    0.00377241 Ra o of Women   0.0924165  0.00868319                0.0872776                                                                   Workers                              Ra o of Technical                                                                   Mo va on of Top                    0.00369803 and Administra ve  0.0897509  0.0085613  Management  0.0867333                              Staff                              Mo va on of                    0.00363094                 0.073188  0.00740714 FDI             0.0856955                              Workers                    0.00350262 Ra o of Workers  0.0769846  0.00706415 Ra o of Exports  0.0783415                               Mo va on of Top                    0.00350031                 0.0730957  0.00692042 Span of Control  0.0632577                              Management                    0.00330279 Span of Control  0.0730181  0.00635151 Ra o of Women  0.0551528                                                                   Ra o of Technical                    0.00326192 Ra o of Exports  0.0674859  0.00625303 and Administra ve  0.0527764                                                                   Staff                              Company Size                    0.00324774 (number of      0.0695187  0.0062338  Ra o of Workers  0.0539102                              employees)                                                                   Reasons for Staff                    0.00318828 Ra o of Graduates  0.0668979  0.00591669             0.0488559                                                                   Turnover                                                                   Number of                    0.00310982 Strategy        0.0563008  0.00566361 management levels  0.0476115                                                                   per employee                              Intensity of                    0.00269444 Mo va on Means  0.0572132  0.00551711 Ra o of Graduates  0.0471201                              Use                    0.00255556 Specificity of Supplies 0.0521837  0.00540293 Foreign Supplies  0.0458394","Castek_1_Castek  23.1.2015  7:37  Stránka 83                         4.8 IMPROVED MODEL FOR ATTRIBUTE SELECTION ON HIGH-DIMENSIONAL ECONOMIC DATA  83                     coefficients. The “Error on subset” means the error of the pseudo-kernel regression                   model that is based on all the features in the preceding rows including the current                   feature. The first three columns represent the values for the Euclidean (L ) distance                                                                                   2                   while the last three columns show the results for the L distance used.                                                                  7                       The higher the DAF coefficient (explained in the previous chapter) of a feature                   is, the more informative (thus more important) the feature is. In the regression                   approach, the DAF feature selection method is applied to minimize the estimated                   error of predicted dependent values for each known company.                       Kernel width is then optimized, starting initially from the estimated average                   distance between any two samples in the available data.                       Table 4-4 shows the impact of the improved model on the results of feature                   selection. The ordering of selected features changes notably, but generally those                   features identified as important using Euclidean distance (L ) are identified as                                                                           2                   important also when using L distance, with most of the difference being in relatively                                            7                   limited order shifts. L distance outperforms L in very small subsets (up to 5 features).                                                          7                                     2                   After that, L is distinctively better than L . This can be observed in up to roughly 25                                                       2                              7                   features, after which the error on subsets becomes very similar (these results are not                   shown due to the paper length limit). The DAF coefficient is, on the other hand, much                   higher while using L distance from the very beginning.                                     7                   Kernel width multiplication constant                   In the paper by Pudil et al. (2013), the default width of all kernels was set to the                   estimated standard deviation of the distances between all pairs of samples in the                   available data set. In Figure 4-18 we suggest that kernel width can be adjusted by                   adding the multiplication constant m. Note that for values m>1 the model gets                   smoother, less prone to over-fitting, but also less sensitive to detail. In contrast, values                   m<1 lead to a more detailed model capable of capturing more detail but at the same                   time with degraded generalization ability.                       In the above-specified paper the constant m was optimized on a full set of features                   and then fixed globally at the beginning of the training process. In Figure 4-23 (and                   also Table 4-5) we show that it is possible to improve the accuracy of the model when                   only a smaller subset of features is used (or searched for), if the constant is optimized                   specifically for the model on the considered subspace.                       The reason for the positive effect of m optimization on subspaces is simple;                   the average distance between points in space increases with increasing dimensionality.                   Applying a sub-space model with an m constant optimized on a full feature set                   leads to a model that is smoother than expected, thus reducing its sensitivity                   to detail.                       Note that marked improvement by a local optimization of m can be expected only                   if the difference between the total number of features and the number of features in                   the considered subspace is large. Only then the inherent difference in distances comes","Castek_1_Castek  23.1.2015  7:37  Stránka 84                   84  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     into play. This effect is observable for subsets of roughly up to 25 features with our                   74-dimensional data.                       The impacts of optimizing the kernel width are presented in the following Table                   4-5. The “DAF” columns and the “Error on subset” have the same meaning as in Table                     Table 4-5: Comparing feature orderings yielded by a model using a globally versus locally optimized                   kernel width multiplier constant. Euclidean distance is used in both cases.                                                                        74‐dimensional data, locally                    74‐dimensional data, globally op mized kernel width mul plier                    constant m=3.06                                   op mized kernel width                                                                      mul plier constant m                                                          Error on subset  Error on subset                                                                                     Locally                                                          containing all  containing all                        DAF              Feature                                    op mized                                                          features up to  features up to  m value                                                           the current  the current                    0.00378051  Span of Control           0.0884389    0.0882787      5                     0.00377241  Ra o of Women             0.0924165    0.0878285      5                                 Ra o of Technical and                    0.00369803                            0.0897509    0.0834008      1.14                                Administra ve Staff                    0.00363094  Mo va on of Workers       0.073188     0.0705265      3.67                     0.00350262  Ra o of Workers           0.0769846    0.0714226      4.22                     0.00350031  Mo va on of Top Management  0.0730957  0.0685935      3.98                                 Number of management levels                    0.00330279                            0.0730181    0.0650337      4.34                                per employee                    0.00326192  Ra o of Exports           0.0674859    0.0608841      4.06                                 Company Size (number of                    0.00324774                            0.0695187    0.0600489      4.4                                employees)                    0.00318828  Ra o of Graduates         0.0668979    0.0600023      4.37                    0.00310982  Strategy                  0.0563008    0.0533632      4.08                                 Intensity of Mo va on Means                    0.00269444                            0.0572132    0.0532684      4.23                                Use                    0.00255556  Specificity of Supplies    0.0521837    0.0506469      3.99","Castek_1_Castek  23.1.2015  7:59  Stránka 85                         4.8 IMPROVED MODEL FOR ATTRIBUTE SELECTION ON HIGH-DIMENSIONAL ECONOMIC DATA  85                     4-4. The first three columns represent the values for the kernel width multiplier                   constant optimized globally while the last three columns show the results for the same                   multiplier constant optimized locally.                    4.8.2 Optimized model performance on 37- and 74-dim data                    We applied the optimization described above to two datasets: the 37-dimensional data                   used in a paper by Pudil et al. (2013) and to newly acquired 74-dimensional data                   representing the same domain by a wider set of differently defined features. In Figure                   4-24 we provide two comparisons. First, we compare model accuracy on a 37-                   dimensional dataset to the accuracy on a 74-dimensional dataset. Second, we compare                   the model accuracy for each of the two datasets in the default setting as described in                   (Pudil et al., 2013) to the model tuned both with respect to the employed distance                   measure and with respect to the locally adjusted multiplication constant (see Section                   4.8.1).                       It is apparent from Figure 4-24 that the proposed improvements to pseudo-kernel                   regression model did not improve the best achievable prediction error, but it did                   notably improve model accuracy on subspaces. With 37-dimensional data, all results                   for subsets of up to 30 features proved to be notably better when the improved model                   was used. With the 74-dimensional data, the most notable improvement took place                   on subspaces of up to roughly half of the total number of features. This means the                    Figure 4-24: Comparing the accuracy of default model to that of the improved model. Comparison                   provided separately for 37- and 74-dimensional dataset representing the same domain. Default                   configuration compared to the best configuration identified in this paper","Castek_1_Castek  23.1.2015  7:37  Stránka 86                   86  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     improvement is achieved when a smaller set of key factors of corporate                   competitiveness is to be identified.                       Also note in Figure 4-24 that the best achievable model setting produces                   practically equal accuracy if all new 74 features are used or if all old 37 features are                   used. This can be explained by mutual statistical dependencies of features which                   become redundant; thus, adding more and more features does not increase the overall                   information value. The new feature set, however, allows the selection of a small subset                   that performs better than an equally sized selected subset of the old set. This is                   apparent in Figure 4-24 for subsets of up to 4 features where the model on 74-                   dimensional data gives a lower prediction error.                       The impacts of extending the original 37-dimensional dataset into a 74-                   dimensional dataset are presented in the following Table 4-6, with the columns having                   the same meaning as in the preceding tables.                    Table 4-6: Top 25 features selected using the optimized model on 74-dim and 37-dim data                     74‐dimensional data, L7 distance, localized  37‐dimensional data, L7 distance, localized                    kernel width mul plica on constant   kernel width mul plica on constant                                               Error on                             Error on                       DAF         Feature                  DAF        Feature                                                subset                               subset                                                                    Ra o of                                                                    Technical and                    0.00869157  Strategy      0.0885253  0.0225594                 0.113963                                                                    Administra ve                                                                    Staff                               Mo va on of                          Expenses on                    0.00868319  Workers       0.0849643  0.0157939  Employee`s     0.106365                                                                    Benefits                                                                    Expenses on                               Mo va on of                    0.0085613                 0.0837816  0.0141935  Employee`s     0.0997067                               Management                                                                    Educa on                                                                    Mo va on of Top                    0.00740714  FDI           0.0788026  0.0141366                 0.0732506                                                                    Management                    0.00706415  Ra o of Exports  0.0749111  0.0134088  Strategy    0.0609535                    0.00692042  Span of Control  0.0632048  0.0118486  FDI         0.0540098                                                                    Ra o of                    0.00635151  Ra o of Women  0.0551528  0.0116693                0.0503014                                                                    Graduates                               Ra o of                               Technical and                    0.00625303                0.0527764  0.0114994  Ra o of Exports  0.0467132                               Administra ve                               Staff                                                                    Number of                                                                    management                    0.0062338  Ra o of Workers  0.0539102  0.0100634               0.0434888                                                                    levels per                                                                    employee","Castek_1_Castek  23.1.2015  7:37  Stránka 87                         4.8 IMPROVED MODEL FOR ATTRIBUTE SELECTION ON HIGH-DIMENSIONAL ECONOMIC DATA  87                                  Reasons for Staff                     Specificity of                    0.00591669                0.0488559  0.010026                  0.0414148                               Turnover                             Supplies                               Number of                    0.00566361  management                          Specificity of                                              0.0476115  0.00971683                0.0405086                               levels per                           Products                               employee                                                                    Company Size                               Ra o of                    0.00551711                0.0471201  0.00963302  (number of    0.0397118                               Graduates                                                                    employees)                                                                    Owners in Top                    0.00540293  Foreign Supplies  0.0458394  0.00932846            0.0349433                                                                    Management                    0.005298   Specificity of                        Stability of                                              0.0431305  0.00908389                0.0356843                               Supplies                             Customers                    0.00515788  Access to                           Rate of Staff                                              0.0415497  0.00904028                0.0359644                               Funding                              Turnover                                                                    Supplier                               Company Size                                                                    Selec on                    0.00509582  (number of    0.0411758  0.00899967                0.0345245                                                                    Criterion: CSR                               employees)                                                                    Compa bility                    0.00498899  Specificity of  0.0404037  0.00886835  Foreign Supplies  0.0341523                               Products                    0.00488013  Level of      0.0390621  0.00855376  Region        0.0344136                               Corrup on                    0.00477958  Maturity of the  0.038239  0.00845204  Legal Form of the  0.0342419                               Company                              Company                                                                    Supplier                                                                    Selec on                    0.00475404  CSR           0.0367709  0.00844075                0.0342001                                                                    Criterion: Quality                                                                    Cer ficate                                                                    OHSAS                               Importance of                    0.00450035                0.0356523  0.00828733  Cer ficate     0.0312972                               Creditors                                                                    Holding                    0.00447213  Stability of                                              0.0343655  0.00822393  CSR           0.030517                               Customers                               Effect of                    0.00442313                                      Assets Level                               Employee`s     0.0337949  0.0079642                 0.0299106                               Benefits                               Intensity of                    0.00442278                                      Stability of                               Mo va on       0.0339987  0.00782862                0.0304842                                                                    Suppliers                               Means Use                    0.0042628  Other Costs    0.0331099  0.00754582  Ownership Type  0.0308387","Castek_1_Castek  23.1.2015  7:37  Stránka 88                   88  4 TESTING APPROACHES AND METHODS BASED ON LEARNING METHODS...                     4.9 Conclusions                      It can be stated that the results presented here confirm the claim of the usefulness of                   applying learning approaches in searching for factors of corporate competitiveness,                   which was stated at ICMLG 2013 in Bangkok (Pudil, 2013). Though the methods of                   machine learning and feature selection (FS) are related to statistical methods in                   particular, they are less strict with respect to assumptions about the data analysed.                       The core idea of how to derive factors of corporate competitiveness is based on                   selecting those features (variables characterizing companies) which have the highest                   importance in a special multivariate regression model predicting the CFP and                   minimizing the error between the predicted and real value of CFP. Therefore, the                   factors of corporate competitiveness have a straightforward meaning – they are just                   those features which have the highest impact on corporate financial performance and                   thus on corporate competitiveness.                       We have described several modifications to the pseudo-kernel regression model                   used in Pudil et al. (2013) for evaluating the importance of corporate competitiveness                   factors. The modifications proved capable of notably improving model accuracy if                   applied on subspaces. In other words, if a small subset of factors is to be evaluated,                   then the improved model allows selecting factors that provide more accurate                   information than subsets selected in the paper by Pudil et al. (2013).                       We have also compared the results on original 37-dimensional data and newly                   acquired 74-dimensional data obtained on the same domain. Though the effort                   invested to define more features failed to result in direct improvement of the best                   achievable accuracy in the full feature space, some newly included features helped to                   yield better results in very small subspaces.                       The implication of our findings for the search for the factors of competitiveness                   is as follows. One cannot expect competitiveness on the corporate level to be a result                   of one particular cause. The whole body of literature on this topic works with the                   notion that competitiveness is a complex phenomenon with multiple causes                   (Beranova, 2008, Andrews et al., 2010 and others). Our results point to this with the                   error on subsets decreasing to the very last feature included and evaluated. This can                   be interpreted in the way that each of the features (company characteristics) has its                   contribution to the prediction of CFP. However, in practice it would be difficult if not                   next to impossible to make changes to a business according to e. g. 74 characteristics                   as in our regression model. A smaller set of characteristics is suitable for this, making                   the improved model more useful as it selects features with better prediction power.                   This means that these characteristics are most important for a given set of companies                   and thus can be regarded as factors of their competitiveness.                       To generalize the contribution of our findings, for a researcher it lies in the                   possibility of processing high-dimensional data in an easier manner and with a better                   reliability of the result. If applied in the field of competitiveness, then the result points","Castek_1_Castek  23.1.2015  7:37  Stránka 89                                                                                   4.9 CONCLUSIONS  89                     at characteristics important for the practitioner. The practitioner can therefore adjust                   his or her own business according to the values of the characteristics found to have                   the strongest influence on the business performance.","Castek_1_Castek  23.1.2015  7:37  Stránka 90","Castek_1_Castek  23.1.2015  7:37  Stránka 91                                                                                                   91                             5 Identifying factors of competitiveness using                      bivariate analyses and linear                       regression analyses                          This chapter explores bivariate associations of the individual variables included in the                   experiments with the financial performance of companies. In addition, it formulates                   partial linear regression models. Both are arranged in units corresponding to the                   division of the original questionnaire survey that followed the logic of the stakeholder                   view of an enterprise. This means that the corporate characteristics are analysed in                   groups related to the owners, employees, customers, suppliers, and business                   environment. However, they are preceded by sections regarding potential internal and                   external factors of competitiveness and a section on the overall approach to the system                   of business management. Each of these units represents an independent sub-chapter                   and a separate partial linear regression model in the following text. These analyses                   serve as the basis for interpreting the results of the DAF experiments, since these do                   not provide simple instructions explaining the influence of the predictors examined,                   as is the case of e.g. linear regression models or t-tests, analyses of variance, or                   correlation analyses.                       Therefore, we will use independent samples t-tests, an analysis of variance,                   correlation analysis, and linear regression models in this chapter, using Pearson’s r,                   Spearman’s r and Kendall’s τ coefficients. While Pearson’s r is preferably used when                                            c                              s                   assumptions of this test are met, due to the direct comparability of the results of the                   correlation analysis with regression models, Spearman’s r is used when the sample                                                                      s                   does not follow bivariate normal distribution but still the relationship between two                   variables is monotonous. Kendall’s τ is used in the analyses where the independent                                                   c                   variable is an ordinal variable with fewer categories, resulting in tied ranks. Kendall’s                   τ should be used in such situations (deVaus, 2002; Field, 2009). Coefficient η will be                    c                   used to report the effect size of associations examined by t-test and by ANOVA and                   is calculated as follows                   for t-test:                                                                  where                                                                  t denotes t-test statistic                                                                  df denotes degrees of freedom","Castek_1_Castek  23.1.2015  7:37  Stránka 92                   92  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     for ANOVA:                             where                   SSA denotes Sum of squares between groups                   SST denotes Total sum of squares)                        All associations examined are evaluated at the level of significance of α = 10%,                   thus reducing the chance of making a Type I error. However, the actual p-values                   observed are reported for each test together with the number of observations involved                   in the particular test, together with the effect size found by this test. Thus, our reader                   can kindly evaluate our results.                     5.1 General characteristics                     Before we start examining the influence of the variables concerned, it is also necessary                   to consider the influence of the general characteristics of enterprises that can affect                   the particular variables or that can modify or disguise their impact on financial                   performance, or those which give the appearance of such an action. These are                   particularly the industry in which the company operates, and the size of the company.                   These two characteristics are usually considered control variables in examining the                   factors of competitiveness or the financial performance of a company. This is true for                   a wide range of studies on completely different areas of financial performance factors.                   We can mention, for example, works by Coles et al. (2012) Structural Models and                   Endogeneity in Corporate Finance: The Link between Managerial Ownership and                   Corporate Performance, Youndt et al. (1996) Human Resource Management,                   Manufacturing Strategy, and Firm Performance, or Powell and Dent-Micallef (1997)                   Information Technology as Competitive Advantage: The Role of Human, Business and                   Technology Resources.                     Effect of company size on the financial performance                    Company size is usually measured by the number of employees, the volume of total                   capital or the volume of total sales. In our case we consider total capital or sales to be                   rather variables describing the response variable, i.e. business performance. Therefore,                   a good representative of company size is the number of employees. However, in our                   sample (as well as in the population), the number of employees is significantly skewed","Castek_1_Castek  23.1.2015  7:37  Stránka 93                                                                        5.1 GENERAL CHARACTERISTICS  93                     with a predominance of values on the left, i.e. in smaller businesses and with                   significant outliers towards large enterprises. Thus, extreme values (up to 5,600                   employees) were Winsorized. In some cases it may be preferable to use categorized                   company sizes, dividing enterprises into categories of 50 to 99 employees, 100 to 249                   employees, and 250 or more employees. As the following table shows, such a division                   is more uniform.                    Table 5-7: Frequency distribution of a categorized company size                         Valid       Frequency       Percent     Valid Percent  Cumula ve Percent                         50–99        128             29.6          29.6         29.6                         100–249      175             40.5          10.5         70.1                         >250         129             29.9          29.9         100.0                         Total        432             100.0        100.0                         Since the vector of financial performance variable and size of a company variable                   measured by the number of employees strongly violates the assumption of two-                   dimensional normality, we use Kendall’s coefficient τ to measure the association                                                                   c                   between the size and the financial performance. The influence of categorized company                   size is measured by an analysis of variance and its effect by coefficient η.                    Table 5-8: The association between the company size and the financial performance                           Variable          Coefficient          Associa on       p (two‐tailed)                    Categorized size          η               0.122            0.046                     Number of                 τ               ‐0.068           0.032                    employees                  c                        Both ways of expressing company size were significantly related to financial                   performance. In both cases, the measure of association is low (one might say trivial                   in the case of the number of employees) and in both cases it is also true that larger                   companies show worse financial performance. The average performance of small                   businesses in the sample is m = 0.416, m = 0.247 for medium-sized businesses, and m                   = 0.117 for large enterprises.","Castek_1_Castek  23.1.2015  7:37  Stránka 94                   94  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     Effect of industry on the financial performance                     The industry in which a company operates can be expressed in our sample at the level                   of the first two digits of CZ NACE, or at a less detailed level as manufacturing versus                   construction. The first division is of course finer, but even for the sample size of 408                   enterprises there are industries in which the number of observations is very low – in                   up to seven categories it is lower than 10. Therefore, the bigger part of our analyses                   uses the less detailed division to manufacturing and construction. However, the table                   below shows associations and p-values for both independent samples t-test                   (manufacturing/construction categories) and analysis of variance (CZ NACE                   categories).                    Table 5-9: The association between the industry and the financial performance                             Variable             Coefficient       Associa on     p (two‐tailed)                    Industry:                       η                    Manufacturing/Construc on                     0.101           0.039                    Industries by the first two digits  η                    of CZ NACE                                    0.325           0.001                        It is obvious that in both approaches the association with financial performance                   is statistically significant. For the less detailed classification of manufacturing and                   construction, the effect of the industry is not very large but still significant. We find a                   higher performance in construction (m = 0.468) than in manufacturing (m = 0.217).                   The effect is larger for the finer classification and it can be described verbally at least                   as medium. If we examined the differences between particular categories, we could                   find statistically significant differences only between certain categories. For example,                   in the field of “Production of electrical machines and equipment” or “Production of                   radio, television and communication equipment and devices”, the average financial                   performance is relatively high, about m = 0.90. On the other hand, in the field of                   “Production of basic metals and fabricated metal products” and “Production of textiles                   and textile products” the average financial performance is relatively low, m = -0.386,                   or m = -0.267, respectively.                     Interaction of company size and industry                    The data in our sample clearly show that there is an association between control                   variables. In construction, the companies are considerably smaller (m = 173) than in                   manufacturing (m = 267), which is a statistically significant difference (p = 0.001).                   Naturally, the question arises whether the zero order relationships, i.e. the size affecting                   financial performance, and industry affects financial performance, are true. This can                   be verified by examining the conditional associations and correlations. Let us assume","Castek_1_Castek  23.1.2015  7:37  Stránka 95                                                                        5.1 GENERAL CHARACTERISTICS  95                     that the industry affects the size but not vice versa. In this case, we must examine the                   authenticity of the association between the industry and financial performance by                   dividing the sample based on the categorized company size (if the variable describing                   industry was an interval, we could use partial correlations), and the authenticity of                   the association between the size and financial performance by dividing the sample                   based on the industry. The following table shows the former conditional associations.                    Table 5-10: The association between the industry and the financial performance, controlling for the                   size of the company: statistics                          Company size / industry => financial performance  Associa on  p                     50–90        Nominal                 η                         n.s.                                 Number of observa ons                120                     100–249      Nominal                 η            0.138        0.071                                  Number of observa ons                171                    250+         Nominal                 η                         n.s.                                  Number of observa ons                120                       The zero order relationship examined is maintained only in the category of                   medium-sized businesses whereas in the remaining categories it is statistically                   insignificant. For medium-sized businesses it is slightly stronger than it seemed to be                   in the whole sample (η = 0.138 vs. η = 0.101). We can assess the substantive differences                   in the performance in various industries and size categories in the following table.                    Table 5-11: The association between the industry and the financial performance, controlling for the                   size of the company: differences in CFP                                      Industry                    Company          (Manufacturing     N     Mean CFP     Std.     Std. Error                    size                                                 Devia on    Mean                                     /Construc on)                                                        92     0.338      1.044      0.109                    50–99            Manufacturing                                     Construc on                                                        28     0.552      0.751      0.142                                                        134     0.193      1.006      0.087                    100–249          Manufacturing                                     Construc on                                                        37     0.531      0.991      0.163                                                       105     0.144      0.944      0.092                    >250             Manufacturing                                     Construc on                                                        15     0.156      0.641      0.166","Castek_1_Castek  23.1.2015  7:37  Stránka 96                   96  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                         The biggest differences in performance based on industry were observed for                   medium-sized companies, while the difference for small companies is less than half                   compared to medium-sized enterprises, and there is almost none difference for large                   companies. Therefore, we cannot say that company size would explain the variability                   of financial performance better than the industry. More likely, the industry explains                   the financial performance only for medium-sized companies. We can illustrate this                   using a model in the chart below.                    Figure 5-25: The effect of industry on financial performance controlled for the company size                                               As mentioned above, it is also necessary to examine the validity of association                   between the company size and financial performance. In the entire sample, this                   associtation was rather weak. The following table shows the conditional association                   between company size and financial performance, if the sample is divided according                   to the industry.                    Table 5-12: The influence of company size on financial performance, controlling for the industry:                   statistics                            Industry / Company size => financial performance  Correla on  p                     Manufacturing   Ordinal                  τ c       ‐0.031      0.386                                    Number of observa ons              329                     Construc on     Ordinal                  τ c       ‐0.122      0.089                                    Number of observa ons              79","Castek_1_Castek  23.1.2015  7:37  Stránka 97                                                                        5.1 GENERAL CHARACTERISTICS  97                         The company size, measured by the number of employees, shows a statistically                   significant relationship with financial performance only in the construction industry.                   Here, however, it is about twice as strong as it was originally throughout the sample.                   On the other hand, this relationship is statistically insignificant in the manufacturing                   industry. Again, we cannot say that the zero-order correlation is false. The third                   variable, the industry, only modifies the effect of the variable originally examined. The                   model in the chart below shows the relationships mentioned above.                    Figure 5-26: The effect of company size on financial performance controlled for the industry                                            When we combine what was mentioned above, our findings then support the                   model of a direct effect of the company size and industry on financial performance,                   which is in both cases modified by a third variable. All the statistically significant                   associations found are shown by the model in the chart below.                    Figure 5-27: The combined effect of company size and industry on financial performance","Castek_1_Castek  23.1.2015  7:37  Stránka 98                   98  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     5.2 Internal competitiveness factors of a company                     The first part of the questionnaire focused on how respondents subjectively perceive                   the potential internal factors of competitiveness. In nine closed questions, the                   respondents rated their company in comparison with its direct competitors, using a                   scale from 1 – a distinctively lower value – to 5 – a distinctively higher value. The                   following is a list of questions with their average values and correlation with the                   financial performance of the company:                    Table 5-13: Variables describing the internal environment of a company: bivariate correlations with                   CFP                       How do you rate, compared  Average                   p                                                          Pearson’s r                  N                     to your compe tors, your…  value                  (two‐tailed)                    Innova on Ac vity         3.37         0.157        0.002        399                    Product Adjustment        3.89         0.100        0.044        404                     Product Quality           3.74         0.129        0.010        403                    Labour Costs              2.94         0.089        0.076        398                     Other Costs               2.95        ‐0.081        0.110        392                    Labour Qualifica on        3.35         0.122        0.014        398                     Customer Care             3.59         0.048        0.343        400                     Access to Funding         3.33         0.150        0.000        379                    Company’s Goodwill        3.52         0.070        0.165        400                           Scale from 1 – a distinctively lower value – to 5 – a distinctively higher value.                       The p (two-tailed) column in the table above shows p-values of two-tailed tests.                   However, the research in this part evaluates directional hypotheses that seek to                   demonstrate that the increasing value of the variable also increases the financial                   performance. Exceptions are Labour Costs and Other Costs, which were expected to                   demonstrate the negative direction of the correlation, i.e. that the financial                   performance increases with the decreasing values of these variables. Nevertheless, this                   trend was not confirmed for Labour Costs, so it is necessary to use the one-tailed p-                   value of p = 0.962 (1-p/2). On the contrary, for other variables, it is possible to divide                   the two-tailed p-value by two, which will show Other Costs and Company’s Goodwill                   statistically significant at the level of α = 10% also.","Castek_1_Castek  23.1.2015  7:37  Stránka 99                                                   5.2 INTERNAL COMPETITIVENESS FACTORS OF A COMPANY  99                         Regarding the size effect of relationships that can be generalized, it ranges from                   trivial/none (Other Costs r = 0.081) to low (Access to Funding r = 0.180). So, it is not                   possible to talk about any important factor of financial performance of a company at                   the level of simple bivariate correlation in this area of company characteristics.                     Multidimensional model                    To assess the degree of the joint effect of the aforementioned independent variables on                   financial performance, we can try to formulate a linear regression model in this form:                   Financial performance = β + β *Innovation Activity + β *Product Adjustment +                                                1                                           0                                                                       2                   β *Product Quality + β *Labour Costs + β *Other Costs + β *Labour Qualification                    3                                        4                                                         5                                                                         6                   + β *Customer Care + β *Access to Funding + β *Company’s Goodwill + β *Industry                                                            9                                        8                      7                                                                                   10                   + β *Company Size Medium-sized + β *Company Size Large                                                      12                      11                       The following assumptions were assessed: appropriate variable type, non-zero                   variance of predictors, no strong multicollinearity, homoscedasticity, independent                   errors, normally distributed errors, independent values of outcome, and linear                   relationship between the outcome and predictors.                       The summary of the model obtained from the forced entry linear regression is                   shown in the following table.                   Table 5-14: Summary of the internal factors regression model                                                                   Change sta s cs                                              Std. Error                             R      Adjusted            R Square    F                      R                        of the                     df1    df2     p                           Square   R Square            Change    Change                                              Es mate                    0.338   0.114    0.083     0.892     0.114    3.666    12    342   0.000                           The value of multiple correlation could be considered moderate, as the model                   explains about 11% of the variability of financial performance. Still, the model is                   significant. Estimates of the parameters of this model are listed in the following table.                       In this case there are fewer variables that statistically significantly affect the                   financial performance at the level of α = 10%. This is true for Innovation Activity,                   Other Costs, and Access to Funding; in addition, it includes all the control variables.                   The higher financial performance – if the values of the other variables remain                   unchanged – is related with by higher Innovation Activity, lower Other Costs, and                   better Access to Funding. Furthermore, the construction industry is more profitable                   than manufacturing (the reference value of zero is represented by the manufacturing                   industry) and the larger the company is, the lower its financial performance is","Castek_1_Castek  23.1.2015  7:37  Stránka 100                  100  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     (measured by relative indicators of ROA and asset growth). Access to Funding and                   Company Size are the strongest predictors in this model, followed by Innovation                   Activity and Industry, being approximately at the same level, while the weakest                   predictor is the level of Other Costs.                    Table 5-15: Coefficients of the internal factors regression model                                                     Unstandardized  Standardized                                                     Coefficients    Coefficients                               Model                                             t      p                                                    B    Std. Error   Beta                     (Constant)                    ‐0.583   0.368               ‐1.587  0.113                     Innova on Ac vity             0.088    0.049      0.098    1.777   0.076                    Product Adjustment            0.053    0.061      0.049    0.873   0.383                     Product Quality               0.082    0.074      0.068    1.111   0.267                    Labour Costs                  0.072    0.056      0.073    1.285   0.200                     Other Costs                   ‐0.120   0.065     ‐0.102    ‐1.852  0.065                    Labour Qualifica on            0.062    0.072      0.051    0.867   0.386                     Customer Care                 ‐0.054   0.059     ‐0.053    ‐0.916  0.360                    Access to Funding             0.163    0.049      0.187    3.308   0.001                     Company’s Goodwill            ‐0.061   0.059     ‐0.064    ‐1.037  0.300                    Industry                      0.213    0.125      0.091    1.705   0.089                    Company size: Medium‐sized vs.                                                  ‐0.275   0.116     ‐0.145    ‐2.377  0.018                    Small                    Company size: Large vs. Small  ‐0.375  0.126     ‐0.184    ‐2.982  0.003                      5.3 External competitiveness factors of a company                      The following set of eight variables focused on how respondents subjectively perceive                   the potential external competitiveness factors. The respondents used another eight                   closed questions to rate their company in comparison with its direct competitors,                   using a scale from 1 – a very low value – to 5 – a very high value. The following is a                   list of questions with their average rating and correlation with the financial                   performance of the company:","Castek_1_Castek  23.1.2015  7:37  Stránka 101                                                   5.3 EXTERNAL COMPETITIVENESS FACTORS OF A COMPANY  101                     Table 5-16: Variables describing the external environment of a company: bivariate correlations with                   CFP                                                            Average               p                                How do you rate…                   Pearson’s r            N                                                            value             (two‐tailed)                    Competitive Rivalry                     4.10     ‐0.133     0.008    404                    Power of Buyers                         3.87     ‐0.065     0.194    404                     Power of Suppliers                      3.27     ‐0.096     0.053    404                     Interest in Employment                  2.99     0.211      0.000    401                    Level of Corruption                     2.28     ‐0.002     0.964    389                     Support from the State                  1.67     0.133      0.008    403                    Support from Municipality/Local Administration  2.01  0.067  0.181   400                     Market Progress                         3.60     0.151      0.003    386                     Scale from 1 – a very low value – to 5 – a very high value. For Market Progress: 1 –                   very narrowing to 5 – very widening.                       The tested hypotheses were not directional for the variables Level of Corruption                   and Market Progress. However, for all the others the direction of the correlation found                   is in line as expected. For this reason, it is again possible to divide the p-values by two,                   and Power of Buyers and Support from Municipality/Local Administration will also                   become statistically significant correlations at the level of α = 10%. Only Level of                   Corruption shows no statistically significant correlation with financial performance.                       We can also note that the factual relationship between both the variables with                   higher p-values and the financial performance is so weak that we cannot talk about                   influencing the financial performance by these variables. As for other variables, their                   effect can be interpreted as very low in the case of Power of Suppliers (r = -0.096), low                   for Competitive Rivalry (r = -0.133), Support from the State (r = 0.133) and Market                   Progress (r = 0.151), and low to medium for Interest in Employment (r = 0.211).                   A higher level of Competitive Rivalry or bargaining Power of Buyers and Suppliers                   hurts the company’s financial performance, while higher Interest in Employment and                   Support from the State and from Municipality/Local Administration as well as the                   widening Market Progress help the financial performance. Again, we cannot talk about                   any important factor of financial performance at the level of a simple bivariate                   correlation in this area of company characteristics.","Castek_1_Castek  23.1.2015  7:37  Stránka 102                  102  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     Multidimensional model                     To assess the degree of joint effect of the aforementioned independent variables on                   financial performance, we can try to formulate a linear regression model in this form:                   Financial Performance = β + β *Competitive Rivalry + β *Power of Buyers +                                                                          2                                                 1                                            0                   β *Power of Suppliers + β *Interest in Employment + β *Level of Corruption +                                           4                    3                                                                       5                   β *Support from the State + β * Support from Municipality/Local Administration +                    6                                             7                   β *Market Progress + β *Industry + β *Company size Medium-sized + β *Company                                                                                  11                                                   10                    8                                       9                   size Large                       The following assumptions were assessed: appropriate variable type, non-zero                   variance of predictors, no strong multicollinearity, homoscedasticity, independent                   errors, normally distributed errors, independent values of outcome, and linear                   relationship between the outcome and predictors.                       The summary of the model obtained from the forced entry linear regression is                   shown in the following table.                   Table 5-17: Summary of the external factors regression model                                                                   Change sta s cs                                              Std. Error                             R      Adjusted            R Square    F                      R                        of the                     df1    df2     p                           Square   R Square            Change    Change                                              Es mate                    0.343   0.118    0.090     0.849     0.118    4.213    11    347   0.000                           As in the case of the internal factors, we could consider the value of multiple                   correlation of 0.343 moderate, as the model explains almost 12% of the variability of                   financial performance. Also, the model is significant. Estimates of the parameters of                   this model are listed in the following in the Table 5-18.                       In this case, most of the variables statistically significantly affect financial                   performance. However, this is not true for Power of Buyers, Power of Suppliers, Level                   of Corruption, and Support from Municipality/Local Administration. As for the                   control variables, the impact of Industry is statistically insignificant.                       The higher financial performance – if the values of the other variables remain                   unchanged – is related with lower Competitive Rivalry, higher Interest in                   Employment, higher Support from the State, and widening Market Progress.                   Increasing Company Size also means a lower financial performance (measured by                   relative indicators of ROA and asset growth). Relatively strong predictors are Interest                   in Employment, Competitive Rivalry, and a shift from a small business to a large                   enterprise. The lowest relative effect can be observed for the bargaining Power of                   Suppliers, followed by Support from the State. Market Progress and a shift from small","Castek_1_Castek  23.1.2015  7:37  Stránka 103                                                   5.3 EXTERNAL COMPETITIVENESS FACTORS OF A COMPANY  103                     to a medium-sized business have a relatively moderate influence. As mentioned above,                   however, the explanatory power of the model as a whole is rather low or medium.                    Table 5-18: Coefficients of the external factors regression model                                                                     Standardized                                                     Unstandardized   Coeffi‐                                                       Coefficients                                 Model                                 cients     t      p                                                              Std.                                                      B                Beta                                                             Error                    (Constant)                       0.152   0.421              0.361   0.719                     Competitive Rivalry              ‐0.162  0.060    ‐0.146    ‐2.714  0.007                     Power of Buyers                  ‐0.003  0.060    ‐0.003    ‐0.052  0.959                    Power of Suppliers               ‐0.090  0.059    ‐0.080    ‐1.533  0.126                     Interest in Employment           0.179   0.062     0.151    2.893   0.004                     Level of Corruption              0.012   0.042     0.016    0.290   0.772                     Support from the State           0.102   0.055     0.106    1.850   0.065                     Support from Municipality/Local                                                     ‐0.027  0.052    ‐0.030    ‐0.513  0.608                    Administration                    Market Progress                  0.153   0.058     0.137    2.646   0.009                     Industry                         0.198   0.125     0.088    1.583   0.114                     Company size: Medium‐sized vs Small  ‐0.242  0.110  ‐0.134  ‐2.198  0.029                     Company size: Large vs Small     ‐0.282  0.121    ‐0.145    ‐2.342  0.020                      5.4 Stakeholder orientation and characteristics                        of an organizational structure                     This part of the questionnaire examined a company as a whole; it did not go into the                   details of individual stakeholder groups, as was the case with the other sections. It                   rather focused on the structure or relations between stakeholder groups in terms of                   company management. If management were singled out as a separate stakeholder                   group, these questions would then belong to the section investigating just","Castek_1_Castek  23.1.2015  7:37  Stránka 104                  104  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     management. The inclusion of this section was based on both the selected stakeholder                   approach to analysing an enterprise, and research into stakeholder management and                   company performance (Berman, 1999) or social and financial performance of a                   company (Preston, O’Bannon, 1997).                    Table 5-19: Contents of the variables describing the stakeholder orientation and characteristics of                   an organizational structure                                   Question               Variable name          Values                     How important is/are for your company…                                                     Importance        1 – unimportant group/5                              owners?                                                     of owners         – very important group                                                     Importance        1 – unimportant group/5                              employees?                                                     of employees      – very important group                                                     Importance        1 – unimportant group/5                              customers?                                                     of customers      – very important group                                                     Importance        1 – unimportant group/5                              suppliers?                                                     of suppliers      – very important group                                                     Importance        1 – unimportant group/5 –                              creditors?                                                     of creditors      very important group                                                     Importance        1 – unimportant group/5 –                              the state?                                                     of the state      very important group                                                     Importance        1 – unimportant group/5 –                              communities?                                                     of communities    very important group                    What is the number of independent                                                     Number of Czech                    branches of your enterprise in the Czech                   Interval                                                     Branches                    Republic?                    What is the number of independent  Number of foreign                                                                               Interval                    branches of your enterprise abroad?  Branches                    What is the number of relatively                                                     Number                    autonomous organizational units of your  of autonomous units  Interval                    enterprise?                    What is the average autonomy                    of the organizational units within   Autonomy              Interval                    the defined categories?                    What is the number of management levels  Number                                                                               Interval                    in the main line of management?  of management levels                    What is the span of control?     Span of control           Interval                                                     Number                    What is the number of management levels                                                     of management levels      Interval                    per one employee?                                                     per employee","Castek_1_Castek  23.1.2015  7:37  Stránka 105                        5.4 STAKEHOLDER ORIENTATION AND CHARACTERISTICS OF AN ORGANIZATIONAL STRUCTURE  105                         The variables included here first assess the importance of the defined interest                   groups (stakeholders) for an enterprise, using a scale from 1 – an unimportant group                   – to 5 – a very important group. Furthermore, the enterprise is described with the                   number of independent branches in the Czech Republic, the number of independent                   branches abroad, the number of relatively autonomous organizational units and their                   average autonomy, the number of management levels, span of control, and the number                   of management levels per one employee. The autonomy of organizational units was                   rated on a scale from 1 – low autonomy to 5 – high autonomy in these areas:                   production program planning, dealings with customers, planning material inputs,                   dealings with suppliers, workforce development planning, and staff selection and                   recruitment. The following is a list of variables with their average rating and correlation                   with the financial performance of the enterprise:                    Table 5-20: Variables describing stakeholder orientation of an enterprise and characteristics of an                   organizational structure: bivariate correlations with CFP                                                          Average                 p                                  Variable                         Kendall’s τ c         N                                                          value              (two‐tailed)                    Importance of Owners                   4.48      0.023     0.510    408                    Importance of Employees                4.05      0.043     0.271    410                     Importance of Customers                4.68      0.013     0.706    410                    Importance of Suppliers                3.79     ‐0.065     0.103    409                     Importance of Creditors                2.73     ‐0.054     0.217    396                     Importance of the State                2.42      0.092     0.021    408                    Importance of Communities              2.58     ‐0.004     0.923    406                    Number of Czech Branches 2             1.23      0.027     0.390    400                     Number of Foreign Branches 2           0.25     ‐0.005     0.812    389                     Number of Autonomous Units 2           1.24      0.025     0.425    386                    Autonomy 2                             1.20      0.036     0.252    403                     Number of Management Levels 2          3.18     ‐0.009     0.808    401                    Span of Control 2                     13.22      0.017     0.612    396                     Number of Management Levels per Employee 2  0.02  0.051    0.116    401                   1                    Scale from 1 – very low to 5 – very high.                   2                    Variables with strongly abnormal two-dimensional distribution.","Castek_1_Castek  23.1.2015  7:37  Stránka 106                  106  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                         Due to the distribution of some variables that strongly fail to meet the two-                   dimensional normality condition, Kendall’s coefficient τ was used to assess the                                                                       c                   bivariate correlations. This coefficient is nonparametric, immune to tied ranks                   (deVaus, 2002), and according to Field (2002) it is a more appropriate estimate of the                   correlation in population than Spearman’s Rho.                       Out of all the fourteen variables tested, only Importance of the State has a                   statistically significant effect on the financial performance. However, its effect on                   financial performance is on the borderline between trivial to no effect and a very low                   effect. Again, we cannot talk about any important factor of financial performance at                   the level of a simple bivariate correlation in this area of enterprise characteristics.                     Multidimensional model                    To assess the degree of joint effect of the aforementioned independent variables on                                                                                  3                   financial performance, we can try to formulate a linear regression model :                   Financial performance = β + β *Importance of Owners + β *Importance of                                                  1                                             0                                                                              2                   Employees + β *Importance of Customers + β *Importance of Suppliers +                                                                 4                                  3                   β *Importance of Creditors + β *Importance of the State + β *Importance of                    5                                                                              7                                                 6                   Communities + β *Number of Management Levels + β *Span of Control + β *                                                                      9                                   8                                                                                          10                   Number of Management Levels per Employee + β *Industry                                                               11                       The following assumptions were assessed: appropriate variable type, non-zero                   variance of predictors, no strong multicollinearity, homoscedasticity, independent                   errors, normally distributed errors, independent values of outcome, and linear                   relationship between the outcome and predictors. Predictors Size Medium-sized and                   Size Large were removed because of collinearity with Number of Management Levels,                   Span of Control, and Number of Management Levels per Employee.                       The summary of the model obtained from the forced entry linear regression is                   shown in the following table.                   Table 5-21: Summary of the regression model describing stakeholder orientation of an enterprise                   and characteristics of its organizational structure                                                                   Change sta s cs                                               Std. Error                             R      Adjusted            R Square    F                      R                        of the                     df1    df2     p                           Square   R Square            Change    Change                                              Es mate                    0.261   0.068    0.039     0.887     0.068    2.349    11    353   0.008                      3  It includes Number of Independent Branches in the Czech Republic, Number of Independent Branches                     Abroad, Number of Relatively Autonomous Organizational Units, Average Autonomy of the Organiza-                     tional Units.","Castek_1_Castek  23.1.2015  7:37  Stránka 107                        5.4 STAKEHOLDER ORIENTATION AND CHARACTERISTICS OF AN ORGANIZATIONAL STRUCTURE  107                         The multiple correlation value of 0.261 is below the medium effect size, as the                   model explains about 7% of the financial performance variability. Still, the model is                   significant. Estimates of the parameters of this model are listed in the following table.                    Table 5-22: Coefficients of the regression model describing stakeholder orientation of an enterprise                   and characteristics of its organizational structure                                                   Unstandardized   Standardized                               Model               Coefficients  Coefficients   t       p                                                  B    Std. Error   Beta                     (Constant)                  ‐0.695   0.494                ‐1.406   0.161                    Importance of Owners        0.059    0.054     0.057      1.092    0.276                     Importance of Employees     0.022    0.062     0.021      0.346    0.729                    Importance of Customers     0.171    0.087     0.114      1.962    0.051                     Importance of Suppliers     ‐0.111   0.060     ‐0.113     ‐1.842   0.066                    Importance of Creditors     ‐0.053   0.040     ‐0.072     ‐1.319   0.188                     Importance of the State     0.127    0.045     0.171      2.849    0.005                    Importance of Communities   ‐0.057   0.047     ‐0.070     ‐1.208   0.228                     Number of Management Levels  ‐0.005  0.054     ‐0.005     ‐0.093   0.926                     Span of Control             0.003    0.005     0.035      0.675    0.500                     Number of Management Levels                                                5.567    3.203     0.092      1.738    0.083                    per Employee                     Industry                    0.223    0.124     0.099      1.801    0.073                        Similarly to the zero order correlations, only a few variables statistically                   significantly affect financial performance. These include Importance of Customers,                   Importance of the State, Number of Management Levels per Employee, and Industry,                   with only Importance of the State at the level of statistical significance α = 0.05. Both                   higher Importance of Customers and higher Importance of the State imply higher                   financial performance of a company in case the values of the other variables remain                   unchanged. Even the variable Number of Management Levels per Employee has a                   positive impact on financial performance. Furthermore, the construction industry is                   more profitable than manufacturing (the reference value of zero is represented by the                   manufacturing industry). The relatively strongest predictor is Importance of the State,","Castek_1_Castek  23.1.2015  7:37  Stránka 108                  108  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     followed by Importance of Customers, while the impact of Industry and Number of                   Management Levels per Employee is similarly strong.                      5.5 Owners                    This part of the questionnaire dealt with the ownership and property structure of the                   company. As Šedová (2007) stated, “a company’s ownership structure significantly                   affects the creation of a certain model of ownership. The individual ownership models,                   applied in countries with market economies, allow different mechanisms of promoting                   the interests of owners.” The relationships and interests of the owners towards the                   company were examined at two levels, as proposed by Kučera (2005): the relationship                   between the owners and other stakeholders, and the relationship of owners with one                   another. The definition of the different types of ownership took into account the                   specifics of exerting ownership in the Czech Republic. The following is a list of                   variables with an explanation of their content:                    Table 5-23: Contents of variables describing the ownership and property structure                               Question                  Variable                 Values                     Is your enterprise part                                             Concern                    Yes/No                    of a concern?                    What is the legal form                              Natural person/Legal                                             Owner’s Legal Form                    of the owner?                                       person/Both                    What is the ownership    Ownership Concentration    Sole owner/Majority                    concentration?                                      owner/More big owners                    Are there any foreign direct                                             FDI                        Yes/No                    investments in the enterprise?                    Are owners whose stake in the                    company exceeds 5% present   Owners in Board of Directors  Yes/No                    in the board of directors?                     Are owners whose stake in the                    company exceeds 5% present   Owners in Supervisory Board  Yes/No                    in the supervisory board?                     Are owners whose stake in the                    company exceeds 5% present   Owners in Top Management  Yes/No                    in the top management?                    What is the level of the principal                                             Assets Level               1 – obsolete/5 – top‐level                    components of tangible assets?","Castek_1_Castek  23.1.2015  7:37  Stránka 109                                                                                       5.5 OWNERS  109                         The characteristics of the variables are significantly heterogeneous here. Part of                   the variables are dichotomous, part are nominal variables of three values, and one of                   them is ordinal, which we will consider quasi-interval for the purpose of linear                   regression. Bivariate associations between the variables of this section and the financial                   performance of a company follow here, and tests of their significance using ANOVA                   and t-test:                   Table 5-24: Variables describing the ownership and property structure: bivariate relationships with CFP                                    Variable              Coefficient  Association  p (two‐tailed)                     Concern                                 η          ‐           n.s.                     Owner’s Legal Form: Natural Person vs. Legal                                                            η        0.138         0.028                    Person                    Owner’s Legal form: Natural Person \& Legal  η                    Person vs. Natural Person                          ‐           n.s.                     Owner’s Legal Form: Natural Person \& Legal  η      ‐           n.s.                    Person vs. Legal Person                    Ownership Concentration                 η          ‐           n.s.                     FDI                                     η          ‐           n.s.                     Owners in Board of Directors            η        0.104         0.035                    Owners in Supervisory Board             η        0.169         0.001                     Owners in Top Management                η        0.116         0.019                    Assets Level                            τ c      0.190         0.001                        The table shows that there is a statistically significant difference between                   companies whose owner is a natural person (m = 0.386) and companies whose owner                   is a legal person (m = 0.128). Higher performance was found in enterprises owned by                   a natural person. The effect size is, however, low (η = 0.138). What also plays a role is                   how the owners are involved in the management of the companies. If the owners are                   present in the board of directors or the supervisory board, the performance of such                   enterprises is statistically significantly lower (m = 0.365 vs. m = 0.125 for the board of                   directors, and m = 0.376 vs. m = -0.005 for the supervisory board). Conversely, if the                   owners are present in top management, the financial performance of such enterprises                   is higher (m = 0.129 vs. m = 0.355). However, once again the effect size is rather low.                   The positive effect of Assets Level on financial performance is low to moderate. Again,                   it is not possible to talk about any important factor of financial performance in the                   area of enterprise characteristics at the level of a simple bivariate association.","Castek_1_Castek  23.1.2015  7:37  Stránka 110                  110  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     Multidimensional model                     To assess the degree of joint effect of the aforementioned independent variables on                   financial performance, we can try to formulate a linear regression model in this form:                   Financial performance = β + β *Concern + β *Owner’s Legal Form Legal Person +                                                            2                                          0                                               1                   β * Owner’s Legal Form Legal Person \& Natural Person + β *Majority Owners +                                                                          4                    3                   β *Big Owners + β *FDI + β *Board of Directors + β *Supervisory Board + β *Top                                                                  8                                            7                                    6                                                                                        9                    5                   Management + β *Assets Level + β *Industry + β *Company Size Medium-sized                                  10                                                   11                                                                12                   + β *Company Size Large                      13                       The following assumptions were assessed: appropriate variable type, non-zero                   variance of predictors, no strong multicollinearity, homoscedasticity, independent                   errors, normally distributed errors, independent values of outcome, and linear                   relationship between the outcome and predictors. Predictors Size Medium-sized and                   Size Large were removed because of collinearity with Number of Management Levels,                   Span of Control, and Number of Management Levels per Employee.                       The summary of the model obtained from the forced entry linear regression is                   shown in the following table.                   Table 5-25: Summary of the regression model describing the ownership and property structure                                                                   Change sta s cs                                              Std. Error                             R      Adjusted            R Square    F                      R                        of the                     df1    df2     p                           Square   R Square            Change    Change                                              Es mate                    0.431   0.186    0.153     0.851     0.186    5.644    13    321   0.000                          In the case of this model, the multiple correlation value of 0.431 ranges from                   medium to a substantial effect. The model explains almost 19% of the variability of                   financial performance. Also, the model is significant. Estimates of the parameters of                   this model are listed in the Table 5-26.                       Ownership concentration and the presence of the FDI are statistically                   insignificant in this model. Furthermore, Industry and the shift from natural persons                   as owners to the mix of both natural and legal persons are also statistically                   insignificant. In the case of the latter, it is probably caused by a small number of                   companies with this mix among limited liability companies and joint stock companies.                       Even this model shows that the larger the company is, the worse its financial                   performance becomes (measured by the relative indicators of ROA and asset growth).                   Notions from bivariate associations that the presence of the owners in the board of                   directors hurts financial performance while the presence of the owners in top                   management helps it are confirmed here (in both cases the reference value of zero is","Castek_1_Castek  23.1.2015  7:37  Stránka 111                                                                                       5.5 OWNERS  111                     represented by the absence of the owners). In addition, financial performance is                   enhanced by higher Assets Level, inclusion in a Concern Structure (the reference value                   of zero means that the company is not part of a concern), and the ownership by natural                   persons only (the reference value of zero is represented by businesses owned by natural                   persons only). The relatively strongest predictor is Assets Level, followed at a                   considerable distance by the inclusion in the Concern structure, Company Size,                   Owners in Top Management, Owners in Board of Directors, and Natural Persons as                   Owners.                    Table 5-26: Coefficients of the regression model describing the ownership and property structure                                                   Unstandardized  Standardized                                                   Coefficients  Coefficients                               Model                                           t        p                                                  B    Std. Error   Beta                     (Constant)                  ‐0.519   0.246               ‐2.111   0.036                     Concern                     0.372    0.146     0.181      2.547   0.011                    Owner’s Legal Form: Natural Per‐                                                ‐0.255   0.148     ‐0.135    ‐1.722   0.086                    son vs Legal Person                    Owner’s Legal form: Natural Person                                                ‐0.161   0.189     ‐0.047    ‐0.851   0.395                    \& Legal Person vs Natural Person                    Ownership Concentration: Majority                                                0.014    0.136     0.006      0.101   0.919                    Owner vs. Sole Owner                    Ownership Concentration: Multiple                                                ‐0.099   0.140     ‐0.053    ‐0.704   0.482                    Big Owners vs. Sole Owner                    FDI                         ‐0.041   0.144     ‐0.020    ‐0.283   0.777                    Owners in Board of Directors  ‐0.208  0.114    ‐0.112    ‐1.817   0.070                     Owners in Supervisory Board  ‐0.169  0.123     ‐0.084    ‐1.373   0.171                    Owners in Top Management    0.300    0.135     0.158      2.215   0.027                     Assets Level                0.277    0.054     0.268      5.162   0.000                    Industry                    0.105    0.122     0.046      0.861   0.390                     Company Size: Medium‐Sized vs.  ‐0.238  0.114  ‐0.126    ‐2.085   0.038                    Small                     Company Size: Large vs. Small  ‐0.304  0.134   ‐0.150    ‐2.261   0.024","Castek_1_Castek  23.1.2015  7:37  Stránka 112                  112  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     5.6 Employees                     This section of the questionnaire focused on several framing questions: what is the                   structure of employees, what is their turnover and what are the reasons for the                    Table 5-27: Contents of variables describing the stakeholder group of employees                                     Question                     Variable      Types and values                     What is the number of employees?       Number of Employees  Interval                    What is the ratio of women?            Ratio of Women    Interval                     What is the ratio of university graduates?  Ratio of Graduates  Interval                     What is the ratio of technical and administrative  Ratio of Technical and                                                                             Interval                    staff?                                 Administrative Staff                    What is the ratio of workers?          Ratio of Workers  Interval                                                            Staff Turnover Rate:  Below 2 %/2 –                    What is the rate of staff turnover?                                                           Low vs. High      10 %/above 10 %                    What is the average frequency of these reasons for                    staff turnover: reorganization, low wage or salary,  Reasons for Staff                    uninteresting work, lack of career development op‐  Turnover  Interval                    portunities, poor workplace relationships, or per‐                    sonal reasons?                    Do you monitor systematically the reasons for   Staff Turnover Moni‐                                                                             Yes/No                    employees’ leaving?                    toring                    What is the proportion of the variable component  Motivation of Top   Interval                    of salary for top management?          Management                     What is the proportion of the variable component   Motivation of Workers Interval                    of wage for workers?                     What is the impact of the variable component   Effect of Motivation  1 – insignificant/5 –                    of wage or salary on staff motivation?  Component of Wage  very high                    What is the average intensity of using motivation   Intensity of Using Mo‐                    devices, such as stock options, transport allowances,  tivation Devices  Interval                    etc.?                    What resources does the company spend on   Expenses on Employee                    employee benefits (as a percentage of labour             Interval                                                           Benefits                    costs)?                    What is the impact of these employee benefits on  Effect of Employee  1 – insignificant/5 –                    staff motivation?                      Benefits          very high                    What resources does the company spend on   Expenses on Employee  Interval                    employee training (as a percentage of labour costs)? Training","Castek_1_Castek  23.1.2015  7:37  Stránka 113                                                                                     5.6 EMPLOYEES  113                     turnover, and how are they motivated? The previous Table 5-27 presents a list of                   variables with an explanation of their contents.                       Most of the variables are interval, three of them are ordinal, and one is                   dichotomous. Interval variables paired with financial performance for the most part                   fail to meet the condition of two-dimensional normality of distribution; therefore we                   use Spearman’s rs coefficient. Only the effect of the Staff Turnover Rate on financial                   performance (this variable takes three values) will be analysed using ANOVA, and                   the effect of Staff Turnover Monitoring on financial performance (this variable takes                   two values) will be analysed with the t-test. The following are bivariate associations                   between variables of this area and financial performance of a company:                    Table 5-28: Variables describing the stakeholder group of employees: bivariate relationships with CFP                                   Variable             Coefficient  Association  p (two‐tailed)  N                     Number of Employees                  r s      ‐0.101      0.041     405                     Ratio of Women                       r s      ‐0.229      0.001     390                    Ratio of Graduates                   r s       0.129      0.010     393                     Ratio of Technical and Administrative Staff  r s  0.114   0.023     394                     Ratio of Workers                     r s      ‐0.114      0.023     394                     Staff Turnover Rate: Low vs. High    η         0.125      0.039     152                    Reasons for Staff Turnover           r s      ‐0.138      0.007     375                     Staff Turnover Monitoring            η          ‐          n.s.     394                     Motivation of Top Management         r s      ‐0.023      0.676     345                    Motivation of Workers                r s       0.065      0.231     345                     Effect of Motivation Component of Wage  r s    0.094      0.064     391                    Intensity of Using Motivation Devices  r s     0.146      0.003     408                     Expenses on Employee Benefits        r s       0.010      0.859     334                    Effect of Employee Benefits          r s       0.018      0.715     393                     Expenses on Employee Training        r s       0.065      0.235     336","Castek_1_Castek  23.1.2015  7:37  Stránka 114                  114  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                         Most of the variables show a statistically significant relationship with the financial                   performance of a company. This is true for Number of Employees, Ratio of Graduates,                   Ratio of Technical and Administrative Staff, Ratio of Workers, Staff Turnover Rate,                   Reasons for Staff Turnover, Effect of Motivation Component of Wage, and Intensity                   of Using Motivation Devices. Although these variables have a statistically significant                   effect on financial performance, these effects are factually weak (r = 0.094 to 0.146).                                                                            s                   Only in the case of Ratio of Women we can talk about an almost medium effect on                   financial performance. This effect is negative (r = -0.229). As far as Staff Turnover                                                             s                   Rate is concerned, a lower Staff Turnover Rate implies a higher average financial                   performance than a higher Staff Turnover Rate (m = 0.358 vs. m = 0.081). Again, we                   cannot talk about any important factor of financial performance at the level of a simple                   bivariate association in this area of enterprise characteristics.                     Multidimensional model                    To assess the degree of joint effect of the aforementioned independent variables on                   financial performance, we can try to formulate a linear regression model. The variable                   Staff Turnover Rate, which is ordinal, will be treated as nominal since it takes only                   three values. The model will be as follows:                   Financial Performance = β + β *Ratio of Women + β *Ratio of Technical and                                                 1                                                                      2                                            0                   Administrative Staff + β *Low Staff Turnover Rate + β *High Staff Turnover Rate +                                        3                                                                   4                   β *Reasons for Staff Turnover + β *Staff Turnover Monitoring + β *Motivation of Top                                                                           7                                                6                    5                   Management + β *Effect of Motivation Component of Wage + β *Intensity of Using                                  8                                                                           9                   Motivation Devices + β *Effect of Employee Benefits + β *Industry + β *Company                                       10                                                                     11                                                                                  12                   Size Medium-sized + β *Company Size Large                                       13                       The following assumptions were assessed: appropriate variable type, non-zero                   variance of predictors, no strong multicollinearity, homoscedasticity, independent                   errors, normally distributed errors, independent values of outcome, and linear                   relationship between the outcome and predictors. The predictor Number of Employees                   was removed because of heterogeneity of variance, and it was replaced by dummy                   variables Company Size Medium-sized and Company Size Large. Predictors Ratio of                   Graduates, Ratio of Technical and Administrative Staff, Ratio of Workers, Motivation                   of Workers, Expenses on Employee Benefits, and Expenses on Employee Training                   were also removed because of variance heterogeneity.                       The summary of the model obtained from the forced entry linear regression is                   shown in the Table 5-29.                       In the case of this model, the multiple correlation value of 0.335 ranges from                   medium to substantial. The model explains about 11% of the variability of financial                   performance and is significant. Estimates of the parameters of this model are listed in                   the Table 5-30.","Castek_1_Castek  23.1.2015  7:38  Stránka 115                                                                                     5.6 EMPLOYEES  115                     Table 5-29: Summary of the regression model describing the stakeholder group of employees                                                                     Change sta s cs                                              Std. Error                             R      Adjusted            R Square    F                      R                        of the                     df1    df2     p                           Square   R Square            Change    Change                                              Es mate                    0.335   0.112    0.077     0.901     0.112    3.177    13    326   0.000                      Table 5-30: Coefficients of the regression model describing the stakeholder group of employees                                                   Unstandardized   Standardized                                                    Coefficients  Coefficients                               Model                                            t        p                                                   B    Std. Error  Beta                    (Constant)                   ‐0.437   0.518               ‐0.844   0.399                     Ratio of Women               ‐0.007   0.003     ‐0.160    ‐2.827   0.005                    Ratio of Technical                                                  0.864   0.321     0.145     2.687    0.008                    and Administrative Staff                    Staff Turnover Rate: Low      0.032   0.123     0.015     0.261    0.794                    Staff Turnover Rate: High    ‐0.017   0.158     ‐0.006    ‐0.106   0.916                     Reasons for Staff Turnover   ‐0.198   0.163     ‐0.070    ‐1.220   0.223                     Staff Turnover Monitoring    ‐0.090   0.105     ‐0.047    ‐0.854   0.394                    Motivation of Top Management  0.000   0.003     ‐0.007    ‐0.130   0.896                    Effect of Motivation Component   0.082  0.055   0.081     1.493    0.136                    of Wage                    Intensity of Using Motivation                                                  0.531   0.194     0.157     2.741    0.006                    Devices                    Effect of Employee Benefits  ‐0.043   0.055     ‐0.045    ‐0.789   0.431                    Industry                      0.036   0.135     0.015     0.268    0.789                     Company Size: Medium‐sized vs.                                                 ‐0.115   0.125     ‐0.060    ‐0.926   0.355                    Small                    Company Size: Large vs. Small  ‐0.226  0.136    ‐0.110    ‐1.653   0.099","Castek_1_Castek  23.1.2015  7:38  Stránka 116                  116  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                         Only four predictors are statistically significant in this model, and one of them –                   the shift in Company Size to a large enterprise – on the borderline of an acceptable p-                   value (p = 0.099). The other three statistically significant predictors are Ratio of Women,                   Ratio of Technical and Administrative Staff, and Intensity of Using Motivation Devices.                   If the values of other variables remain constant, a higher Ratio of Women decreases                   financial performance of a company, whereas a higher Ratio of Technical and                   Administrative Staff and higher average Intensity of Using Motivation Devices increases                   it. Company size has, as usual, a negative impact on financial performance. As far as the                   relative effect on financial performance is concerned, Ratio of Women, Intensity of Using                   Motivation Devices, and Ratio of Technical and Administrative Staff have a very similar                   effect. On the other hand, Company Size has a lower relative effect.                     5.7 Customers                     Customers as a stakeholder group are mentioned in all the literature of stakeholder theory.                   In the vast majority of empirical studies they are referred to as the most important                   stakeholder group (e.g. Šimberová, 2008), which is also one of the findings of this                   research. As Klapalová (2008) noted, many authors have worked on customer orientation                   as a factor of long-term business success since 1950s, including Peter Drucker among                   others. As for more recent authors focusing on market-orientation, i.e. including                   customer-orientation, we can name e.g. Kohli et al. (1993) or Narver and Slater (1990).                       In this section, the questionnaire provided us with 70 variables focused on the                   following areas: business strategy, long-term relationships with customers and their                   stability, their territorial structure, and specificity of company products. It can also be                   repeated from the other sections of the questionnaire that the researchers were                   determining the importance of customers for a company, level of customer care, their                   bargaining power, degree of flexibility in adjusting products to customer demands,                   level of innovation activity, quality assessment, and evaluating goodwill or brand of a                   company.                       The above-mentioned variables from this section of the questionnaire were                   transformed into six key variables, whose meaning is explained in the Table 5-31.                       Three of the variables are nominal: Strategy, Strategy Focus and Exports. The                   other variables are interval: Stability Buyers, Share of Exports and Product Specificity.                   Because the distribution of their values is very different from normal (bimodal for                   Product Specificity, multimodal for Stability of Customers, and very positively skewed                   for Exports), we measure their relationship with financial performance using the τ c                   coefficient. Since a large number of companies do not export, we also test the effect                   on financial performance based on the division of businesses into two groups:                   exporting and non-exporting. In this case and in the case of the variable Strategy we                   will use the t-test and ANOVA. The following are bivariate associations between the                   variables from this field and financial performance of a company:","Castek_1_Castek  23.1.2015  7:38  Stránka 117                                                                                    5.7 CUSTOMERS  117                     Table 5-31: Contents of variables describing customers of a company                               Question              Variable             Types and values                     What business strategy does  Strategy      Differentiation/Differentiation                    your company follow?                       focus/Cost leader/Cost leader focus                     Strategy Focus Yes/No    Strategy Focus    Yes/No                    What is the stability of your   Stability of Customers  Interval                    customers?                     What is the share of your   Share of Exports  Interval                    foreign customers?                    Does your company have any                                             Exports           Yes/No                    foreign customers?                    What is the ratio of specific                                             Product Specificity  Interval                    products to all your products?                    Table 5-32: Variables describing customers: bivariate relationships with CFP                                                                                  p                                 Variable              Coefficient  Association           N                                                                             (two‐tailed)                    Strategy: Cost Leadership vs.                                                          η         0.157      0.057     182                    Differentiation Focus                    Strategy: Differentiation vs.                                                          η         0.157      0.085     204                    Differentiation Focus                    Strategy: Cost Focus vs. Differentiation Focus              n.s.                     Strategy: Focus Yes/No                η         0.138      0.010     351                    Strategy: Cost/Differentiation                              n.s.                     Stability of Customers                τ c       0.136      0.001     393                    Share of Exports                      τ c      ‐0.056      0.124     376                     Exports: Yes/No                       η         0.128      0.013     376                     Product Specificity                   τ c       0.119      0.001     387                        Besides the original form of the variable measuring the Share of Exports on all                   products, all the other variables show a statistically significant association with                   financial performance of the company. It can be considered even in the case of Share                   of Exports if it is measured only Yes/No (the number of completely non-exporting","Castek_1_Castek  23.1.2015  7:38  Stránka 118                  118  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     companies is 89 out of 376, for which this information is available). The average                   performance of non-exporting companies (m = 0.454) is significantly higher than the                   average performance of exporting companies (m = 0.170). As far as Strategies are                   concerned, the highest performance can be observed in companies that pursue the                   strategy of Differentiation Focus (m = 0.464), followed by companies pursuing the                   strategy of Cost Focus (m = 0.261), then companies with the Differentiation Strategy                   (m = 0.144), and the lowest performance in our sample was found in companies                   pursuing the strategy of Cost Leadership (m = 0.103). There are statistically significant                   differences between strategies Cost Leadership and Differentiation Focus, and between                   strategies Differentiation and Differentiation Focus. No statistically significant                   difference was found between the two strategies oriented on costs and the two                   strategies oriented on differentiation; however, there is a statistically significant                   difference between businesses pursuing attention-focused strategies Focus, which have                   a higher average performance (m = 0.384) than the businesses pursuing strategies                   without this focused attention, whose average performance is lower (m = 0.126). Other                   variables that affect financial performance positively include Stability of Customers                   and Product Specificity. Nevertheless, it should be noted that although these                   associations are statistically significant, their factual significance, effect size, is very                   low. Again, we cannot talk about any important factor of financial performance at the                   level of simple bivariate associations in this area of enterprise characteristics.                     Multidimensional model                    To assess the degree of joint effect of the aforementioned independent variables on                   financial performance, we can try to formulate a linear regression model. The variable                   Exports will be included in its dichotomous form. The variable Strategy will be                   included in the form of Strategy Focus Yes/No, since although its impact on financial                   performance is lower, it is statistically significant at the more broadly accepted                   statistical significance level (α = 10%). Hence, the model will be as follows:                   Financial Performance = β + β *Strategy Focus + β *Stability of Customers +                                                 1                                            0                                                                    2                   β *Exports Yes/No+ β *Product Specificity + β *Industry + β *Company Size                    3                                                                5                                                                              6                                        4                   Medium-sized + β *Company Size Large                                   7                       The following assumptions were assessed: appropriate variable type, non-zero                   variance of predictors, no strong multicollinearity, homoscedasticity, independent                   errors, normally distributed errors, independent values of outcome, and linear                   relationship between the outcome and predictors.                       The summary of the model obtained from the forced entry linear regression is                   shown in the following table.","Castek_1_Castek  23.1.2015  7:38  Stránka 119                                                                                    5.7 CUSTOMERS  119                     Table 5-33: Summary of the regression model describing the stakeholder group of customers                                                                     Change sta s cs                                              Std. Error                             R      Adjusted            R Square    F                      R                        of the                     df1    df2     p                           Square   R Square            Change    Change                                              Es mate                    0.311   0.097    0.076     0.903     0.097    04.641   7     303   0.000                          The multiple correlation value of 0.311 is medium in the case of this model. The                   model explains less than 10% of the financial performance variability. Still, the model                   is significant. Estimates of the parameters of this model are listed in the following table.                    Table 5-34: Coefficients of the regression model describing the stakeholder group of customers                                                                      Standardized‐                                            Unstandardized Coefficients                  p                                                                     Coefficients                            Model                                                  t    (two‐                                                                                       tailed)                                                B        Std. Error    Beta                    (Constant)                ‐0.327       0.299                 ‐1.094  0.275                    Strategy Focus Yes/No     ‐0.137       0.108       ‐0.073    ‐1.271  0.205                     Stability of Customers    0.201        0.064       0.180     3.146  0.002                    Exports Yes/No            ‐0.278       0.155       ‐0.125    ‐1.788  0.075                     Product Specificity       0.003        0.001       0.118     2.091  0.037                     Industry                  0.182        0.161       0.077     1.128  0.260                    Company Size: Medium‐sized                                              ‐0.162       0.123       ‐0.086    ‐1.312  0.190                    vs. Small                    Company Size: Large vs.   ‐0.205       0.140       ‐0.097    ‐1.469  0.143                    Small                         Statistically significant predictors in this model include Stability of Customers,                   Exports and Product Specificity. Both Stability of Customers and Product Specificity                   have a positive impact on the financial performance of a company if the values of the                   other variables remain unchanged. Conversely, if a company exports, its financial                   performance is hurt (the reference value of zero is represented by non-exporting                   companies). The relative power of the individual predictors is highest for Stability of                   Customers and lowest for Exports and Product Specificity.","Castek_1_Castek  23.1.2015  7:38  Stránka 120                  120  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     5.8 Suppliers                     Supplier relationships management is very important in strategies aimed at costs                   (Gaddle, Hakansson, 2002) as well as strategies aimed at quality. There are studies                   examining the relationship of supplier stability and corporate competitiveness                   (O’Toole, Donaldson, 2000), supplier specialization and competitiveness (Hope,                   Spencer, 2001), or the method of selecting suppliers and company competitiveness                   (Kannan, Tan, 2004). Therefore, the variables verified here examine – as an analogy                   to the group of customers – the long-term nature of the relationship, its stability,                   territorial structure of suppliers, and specificity of supplies. Furthermore, criteria for                   selecting new suppliers were also examined. This section of the questionnaire provided                   us with the total of 97 variables that were transformed into 11 variables listed below,                   whose meaning is explained in the following table.                    Table 5-35: Contents of variables describing suppliers of a company                                Question                   Variable           Types and values                     What is the stability of your suppliers? Stability of suppliers  Interval                     What is the percentage of supplies                                                 Foreign Supplies       Interval                    from abroad?                    What is the proportion of specific                                                 Specificity of Supplies  Interval                    supplies to total supplies?                    How important is price as a criterion   Supplier Selection Criterion:  1 – totally unimportant/5                    for selecting suppliers?     Price                  – very important                    How important are the payment terms Supplier Selection Criterion:  1 – totally unimportant/5                    as a criterion for selecting suppliers?  Payment Terms  – very important                    How important are other terms of                                                 Supplier Selection Criterion:  1 – totally unimportant/5                    delivery as a criterion for selecting                                                 Other Terms of Delivery  – very important                    suppliers?                    How important is product quality as   Supplier Selection Criterion:  1 – totally unimportant/5                    a criterion for selecting suppliers?  Product Quality  – very important                    How important is a quality certificate   Supplier Selection Criterion:  1 – totally unimportant/5                    as a criterion for selecting suppliers?  Quality Certificate  – very important                    How important is a supplier’s history   Supplier Selection Criterion:  1 – totally unimportant/5                    as a criterion for selecting suppliers?  Supplier’s History  – very important                    How important are references as   Supplier Selection Criterion:  1 – totally unimportant/5                    a criterion for selecting suppliers?  Reference     – very important                    How important is the compatibility                                                 Supplier Selection Criterion:  1 – totally unimportant/5                    of CSR activities as a criterion                                                 CSR Compatibility      – very important                    for selecting suppliers?","Castek_1_Castek  23.1.2015  7:38  Stránka 121                                                                                      5.8 SUPPLIERS  121                         The first three variables are interval while the others are ordinal. Because the                   distribution of values of the interval variables is very different from normal, similarly to                   the variables describing the stakeholder group of customers (bimodal for Specificity of                   supplies, multimodal for Stability of Suppliers, and very positively skewed towards                   Foreign Supplies), we will use the τ coefficient to measure their correlation with                                                   c                   financial performance. Since many businesses have no supplies from abroad, we will                   also test the relationship of financial performance and businesses classified into two                   groups: with foreign supplies and without them. In this case, the t-test will be used. The                   following are bivariate associations between the variables of this area and financial                   performance of a company:                    Table 5-36: Variables describing suppliers of a company: bivariate relationships with CFP                                                                               p (two‐                                Variable           Coefficient  Association             N                                                                              tailed)                    Stability of Suppliers             τ c        0.064       0.058     402                     Foreign Supplies                   τ c        ‐0.022      0.517     390                    Foreign Supplies: Yes/No           η                       n.s.                     Specificity of Supplies            τ c        0.013       0.707     390                    Supplier Selection Criterion: Price  r        ‐0.110      0.027     403                    Supplier Selection Criterion: Payment  r      ‐0.162      0.001     401                    terms                    Supplier Selection Criterion: Other  r        ‐0.037      0.455     401                    Terms of Delivery                    Supplier Selection Criterion: Product  r      0.083       0.098     403                    Quality                    Supplier Selection Criterion: Quality Cer‐  r  ‐0.010     0.846     401                    tificate                    Supplier Selection Criterion: Supplier’s  r   0.049       0.331     401                    History                    Supplier Selection Criterion: Reference  r    0.108       0.031     401                     Supplier Selection Criterion: CSR com‐                                                       r          0.147       0.003     398                    patibility                       Financial performance statistically significantly correlates with most of the                   Supplier Selection Criteria, i.e. Price, Payment Terms, Reference, and CSR                   Compatibility. A worse but still acceptable p-value is found in Product Quality as a                   Supplier Selection Criterion, and in Stability of Suppliers. Product Quality is the least                   significant even in the factual aspect (r = 0.083), which also applies to Stability of","Castek_1_Castek  23.1.2015  7:38  Stránka 122                  122  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     Suppliers (τ = 0.064). Other associations can be described as at least factually weak.                             c                   Unlike in the stakeholder group of customers, if we recode the interval variables of                   Stability of Suppliers, Foreign Supplies and Specificity of Supplies into Yes/No or                   High/Low, we do not reach statistically significant associations for these recoded                   variables describing the stakeholder group of suppliers. Again, we cannot talk about                   any important factor of financial performance at the level of a simple bivariate                   association in this area of enterprise characteristics.                     Multidimensional model                    To assess the degree of joint effect of the aforementioned independent variables on                   financial performance, we can try to formulate a linear regression model. The variable                   Foreign Supplies will be included in a dichotomous form, as the original variable does                   not show a linear correlation to financial performance. For the same reason, the                                                                                  4                   variable Specificity of Supplies will be included in the form of Low/High . Hence, the                   model will be as follows:                   Financial performance = β + β *Stability of Suppliers + β *Foreign Supplies +                                                 1                                            0                                                                          2                   β *Specificity of Supplies + β *Supplier Selection Criterion: Price + β *Supplier                    3                                                                                    5                                              4                   Selection Criterion: Payment Terms + β *Supplier Selection Criterion: Other Terms                                                      6                   of Delivery + β *Supplier Selection Criterion: Product Quality + β *Supplier Selection                                                                            8                                7                   Criterion: Quality Certificate + β *Supplier Selection Criterion: Supplier’s History +                                                9                   β *Supplier Selection Criterion: Reference + β *Supplier Selection Criterion: CSR                                                             11                    10                   Compatibility + β *Industry + β *Company Size Medium-sized + β *Company                                   12                                                 13                                                                                  14                   Size Large                       The following assumptions were assessed: appropriate variable type, non-zero                   variance of predictors, no strong multicollinearity, homoscedasticity, independent                   errors, normally distributed errors, independent values of outcome, and linear                   relationship between the outcome and predictors.                       The summary of the model obtained from the forced entry linear regression is                   shown in the following table.                   Table 5-37: Summary of the regression model describing the stakeholder group of suppliers                                                                   Change sta s cs                                              Std. Error                             R      Adjusted            R Square    F                      R                        of the                     df1    df2     p                           Square   R Square            Change    Change                                              Es mate                    0.387   0.149    0.093     0.968     0.149    2.636    14    210   0.001                     4  Low specificity = 0 – 10 % of specific supplies, High specificity = 90 – 100 % of specific supplies.","Castek_1_Castek  23.1.2015  7:38  Stránka 123                                                                                      5.8 SUPPLIERS  123                         The multiple correlation value of 0.387 ranges from medium to substantial in the                   case of this model, which explains little bit less than 15% of financial performance                   variability. Also, the model is significant. Estimates of the parameters of this model                   are listed in the following table.                    Table 5-38: Coefficients of the regression model describing the stakeholder group of suppliers                                                Unstandardized   Standardized                                                Coefficients   Coefficients                            Model                                             t        p                                               B      Std. Error  Beta                    (Constant)               ‐1.054    0.787                ‐1.339    0.182                     Stability of Suppliers   0.155     0.094      0.112     1.648     0.101                    Foreign Supplies: Yes/No  ‐0.155   0.174     ‐0.067     ‐0.891    0.374                     Specificity of Supplies  ‐0.044    0.139     ‐0.021     ‐0.315    0.753                    Supplier Selection Criterion:  ‐0.182  0.101  ‐0.133    ‐1.805    0.073                    Price                    Supplier Selection Criterion:  ‐0.078  0.081  ‐0.072    ‐0.955    0.341                    Payment Terms                    Supplier selection criterion:                                             ‐0.143    0.084     ‐0.126     ‐1.714    0.088                    Other Terms of Delivery                    Supplier Selection Criterion:                                             0.384     0.143      0.190     2.684     0.008                    Product Quality                    Supplier Selection Criterion:                                             ‐0.020    0.066     ‐0.021     ‐0.310    0.757                    Quality Certificate                    Supplier Selection Criterion:                                             ‐0.015    0.080     ‐0.013     ‐0.182    0.856                    Supplier’s History                    Supplier Selection Criterion:  0.139  0.078   0.125     1.792     0.075                    Reference                    Supplier Selection Criterion:  0.150  0.057   0.181     2.646     0.009                    CSR Compatibility                    Industry                 0.246     0.205      0.090     1.203     0.230                     Company size: Medium‐sized  ‐0.247  0.157    ‐0.120     ‐1.576    0.117                    vs. Small                    Company size: Large vs. Small  ‐0.317  0.177  ‐0.139    ‐1.792    0.075","Castek_1_Castek  23.1.2015  7:38  Stránka 124                  124  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                         Similarly to the bivariate associations, the effect of these supplier selection criteria                   is statistically significant: Price, Product Quality, Reference, and CSR Compatibility.                   The effect of Payment Terms as a selection criterion is no longer statistically significant;                   instead, the effect of Other Terms of Delivery is statistically significant. These Other                   Terms of Delivery and Price have a negative impact on financial performance, in                   contrast to e.g. Product Quality, which is relatively the strongest predictor of financial                   performance. Stability of Suppliers, which was statistically significant (even though                   at a lower level of statistical significance, p = 0.064), is now narrowly unacceptable                   even at the level of α = 10%. Out of the general characteristics of enterprises, financial                   performance is influenced in this model also by a shift of the company size from                   medium-sized to large, while even here the direction is negative. In terms of the                   relative power of predictors, the strongest predictor is Quality as a supplier selection                   criterion, followed closely by CSR compatibility as a supplier selection criterion, and                   the remaining statistically significant predictors follow after approximately the same                   interval.                      5.9 Corporate social responsibility                    The last section of the questionnaire examined what forms of social responsibility                   enterprises use to become engaged in what areas, and also what codes (e.g. ethical)                   they have. This was actually a way of expressing corporate social performance, which                   has been demonstrated many times as a factor of competitiveness (e.g. a meta-analysis                   by Allouche, Laroche, 2005).                       The variables from this section were transformed into two, i.e. how many forms                   of CSR activities a company is engaged in, and whether a company has at least one                   code. No company indicated that it was not engaged in any form of CSR activities;                   the maximum was six different CSR activities. Whether a company has at least one                   code is a dichotomous variable; therefore, a t-test will be used.                    Table 5-39: Variables describing CSR activities of a company: bivariate relationships with CFP                         Variable      Coefficient    Association  p (two‐tailed)      N                          CSR             r            0.153          0.002          392                       Ethical code       η                           n.s.           394                        Only the number of CSR activities is statistically significantly related to financial                   performance. The effect of the number of CSR activities on financial performance can                   be described as weak, so even in this area there is no important factor of corporate                   competitiveness.","Castek_1_Castek  23.1.2015  7:38  Stránka 125                                                                  5.9 CORPORATE SOCIAL RESPONSIBILITY  125                     Multidimensional model                     To assess the degree of joint effect of the aforementioned independent variables on                   financial performance, we can try to formulate a linear regression model. The model                   will be as follows:                   Financial Performance = β + β *CSR + β *Ethical Code + β *Industry + β *Company                                                                                   4                                                                      3                                          0                                                      2                                              1                   Size Medium-sized + β *Company Size Large                                       5                       The following assumptions were assessed: appropriate variable type, non-zero                   variance of predictors, no strong multicollinearity, homoscedasticity, independent                   errors, normally distributed errors, independent values of outcome, and linear                   relationship between the outcome and predictors.                       The summary of the model obtained from the forced entry linear regression is                   shown in the following table.                   Table 5-40: Summary of the regression model describing corporate social performance                                                                     Change sta s cs                                              Std. Error                             R      Adjusted            R Square    F                      R                        of the                     df1    df2     p                           Square   R Square            Change    Change                                              Es mate                    0.235   0.055    0.043     0.928     0.055    4.388    5     375   0.001                         The multiple correlation value of 0.235 ranges from low to medium in the case of                   this model, with the model explaining less than 6% of financial performance                   variability. Still, the model is significant. Estimates of the parameters of this model are                   listed in the following table.                    Table 5-41: Coefficients of the regression model describing corporate social performance                                                     Unstandardized  Standardized                                                      Coefficients  Coefficients                                Model                                            t      p                                                     B    Std. Error  Beta                    (Constant)                     ‐0.009   0.150              ‐0.060  0.952                    CSR                             0.158  0.046      0.182    3.431   0.001                     Ethical Code                   ‐0.029   0.100    ‐0.015    ‐0.287  0.774                    Industry                        0.178   0.120     0.075    1.478   0.140                    Company Size: Medium‐sized vs. Small  ‐0.194  0.114  ‐0.101  ‐1.694  0.091                    Company Size: Large vs. Small  ‐0.375  0.128     ‐0.178    ‐2.922  0.004","Castek_1_Castek  23.1.2015  7:38  Stránka 126                  126  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                         Similarly to the bivariate associations, only the effect of the number of CSR                   activities is statistically significant. If the values of the other variables remain                   unchanged, a higher number of CSR activities has a positive effect on the financial                   performance of a company. The effect of Company Size is also statistically significant,                   since it is still true that the larger a company is, the lower its financial performance                   becomes. The number of CSR activities is a relatively slightly stronger predictor than                   a shift in Company Size to large and considerably stronger than a shift in Company                   Size to medium-sized.                     5.10 Comprehensive model                     In the preceding section we examined the sub-models of financial performance that                   always focused on one area of a business. Now we will try to construct a model of the                   predictors that were statistically significant in the individual sub-models. The number                   of such predictors exceeds 33, which is a relatively high number for a regression model                   using the available number of measurements. Therefore, we will treat missing values                   excluding missing values pairwise and not list wise as we have thus far. We will also                   rely on assertions by Green (1991) concerning the minimum accepted sample size.                   Green postulates that for an overall fit of a regression model, the minimum sample                   size is 50 + 8*p, where p is the number of predictors. In our case this would mean the                   need for 314 observations. Another rule set by Green is that if we want to test                   individual predictors, which is our case, there is a need for 104 + p observations. This                   would make the need for 137 observations in our case. A more sophisticated rule is                   set by Miles and Shevlin (2001). This takes into account the expected effect of the                   model. A higher expected effect results in a need of a lower number of observations.                   We expect a rather large effect, which would require approximately 100 observations,                   according to Miles and Shevlin. However, the actually obtained effect is rather                   medium-sized, resulting in a need for approximately 250 observations. All of these                   rules are met, as there are between 351 and 409 observations in this regression model.                       The discussed model will therefore be tested as follows:                   Financial performance = β + β *Innovation Activity + β *Other Costs + β *Access                                                                                     3                                                                     2                                               1                                           0                   to Funding + β *Competitive Rivalry + β *Interest in Employment + β *Support from                                                      5                                4                                                                               6                   the State + β *Market Progress + β *Importance of Customers + β *Importance of                                                  8                                                                              9                              7                   the State + β *Concern + β *Owner’s Legal Form: Legal Person + β *Owner’s Legal                                           11                                                                              12                              10                   Form: Natural Person \& Legal Person + β *Owners in Board of Directors+                                                            13                   β *Owners in Top Management + β *Assets Level + β *Ratio of Women + β *Ratio                                                                  16                                                                                      17                    14                                                  15                   of Technical and Administrative Staff + β *Intensity of Using Motivation Devices +                                                       18                   β *Strategy Focus + β *Stability of Customers + β *Exports Yes/No + β *Product                                                                21                    19                                       20                                                                                   22                   Specificity + β *Supplier Selection Criterion: Price + β *Supplier Selection Criterion:                               23                                                                  24                   Other Terms of Delivery + β *Supplier Selection Criterion: Product Quality +                                              25                   β *Supplier Selection Criterion: Reference + β *Supplier Selection Criterion: CSR                                                             27                    26","Castek_1_Castek  23.1.2015  7:38  Stránka 127                                                                         5.10 COMPREHENSIVE MODEL  127                     Compatibility + β *CSR + β *Industry + β *Company Size Medium-sized +                                                             30                                              29                                    28                   β *Company Size Large                    31                       The following assumptions were assessed: appropriate variable type, non-zero                   variance of predictors, no strong multicollinearity, homoscedasticity, independent                   errors, normally distributed errors, independent values of outcome, and linear                   relationship between the outcome and predictors. The predictor Number of                   Management Levels per Employee was removed because of collinearity with Company                   Size. Two observations were removed because of an undue large influence on the                   regression model. Their standardized residual was more than 3.5.                       The summary of the model obtained by the forced entry linear regression is in                   the next table.                    Table 5-42: Summary of the comprehensive regression model                                                                     Change sta s cs                                              Std. Error                             R      Adjusted            R Square    F                      R                        of the                     df1    df2     p                           Square   R Square            Change    Change                                              Es mate                    0.551   0.304    0.235     0.832     0.304    4.399    31    312   0.000                          The multiple correlation value of 0.551 is substantial in the case of this model.                   The model explains over 30% of financial performance variability. Also, the model is                   significant. When compared with the sub-models, it is obvious that this                   comprehensive model can explain a much larger proportion of the variability of the                   response variable. Estimates of the parameters of this model are listed in the Table                   5-43.                       Approximately half of the predictors tested have statistically significant effects on                   financial performance of a company. In all of them, the directions of action are                   consistent with those found in the sub-models. Hence, if the values of the other                   variables remain unchanged, greater financial performance is caused by lower                   Competitive Rivalry, widening Market Progress, greater Importance of the State,                   Owner’s Legal Form as a Natural Person, the absence of Owners in Board of Directors,                   higher Assets Level, lower Ratio of Women, higher Ratio of Technical and                   Administrative Staff, higher Intensity of Using Motivation Devices, emphasis on                   Strategy Focus (either Cost Leadership Focus or Differentiation Focus), higher                   Stability of Customers as long as the company does not export its products, if it does                   not consider Other Terms of Delivery important as a supplier selection criterion, and                   if it is rather smaller than greater.                       The relatively strongest predictor is clearly Assets Level. The other predictors,                   whose relative strength is approximately equal, follow after a considerable interval.","Castek_1_Castek  23.1.2015  7:38  Stránka 128                  128  5 IDENTIFYING FACTORS OF COMPETITIVENESS USING BIVARIATE ANALYSES...                     Table 5-43: Coefficients of the comprehensive regression model                                                             Unstandardized   Standardized                                                              Coefficients  Coefficients                                   Model                                               t     p                                                             B    Std. Error  Beta                (Constant)                                 ‐1.845  0.743             ‐2.485 0.013                 Innovation Activity                        ‐0.014  0.049     ‐0.016  ‐0.288 0.773                Other Costs                                ‐0.098  0.060     ‐0.080  ‐1.623 0.106                Access to Funding                           0.048  0.047     0.055   1.025  0.306                Competitive rivalry                        ‐0.130  0.061     ‐0.112  ‐2.131 0.034                Interest in Employment                      0.071  0.064     0.057   1.100  0.272                 Support from the State                      0.061  0.054     0.058   1.137  0.256                Market progress                             0.113  0.058     0.098   1.945  0.053                Importance of Customers                     0.023  0.079     0.015   0.290  0.772                Importance of the state                     0.069  0.041     0.088   1.675  0.095                Concern                                     0.156  0.130     0.074   1.199  0.232                Owner’s legal form: Natural Person vs. Legal Person  ‐0.221  0.131  ‐0.115  ‐1.681 0.094                 Owner’s Legal Form: Natural Person \& Legal Person vs.                                                           ‐0.004  0.195     ‐0.001  ‐0.020 0.984                Natural Person                Owners in Board of Directors               ‐0.183  0.100     ‐0.096  ‐1.838 0.067                Owners in Top Management                    0.187  0.121     0.097   1.548  0.123                 Assets Level                                0.189  0.062     0.175   3.065  0.002                Ratio of Women                             ‐0.004  0.003     ‐0.097  ‐1.748 0.081                Ratio of Technical and Administrative Staff  0.685  0.307    0.114   2.231  0.026                Intensity of Using Motivation Devices       0.330  0.185     0.096   1.787  0.075                 Strategy FOCUS                             ‐0.169  0.098     ‐0.089  ‐1.714 0.088                Stability of Customers                      0.116  0.059     0.106   1.979  0.049                Exports Yes/No                             ‐0.268  0.138     ‐0.120  ‐1.936 0.054                Product Specificity                         0.001  0.001     0.029   0.551  0.582                Supplier Selection Criterion: Price         0.030  0.071     0.022   0.415  0.679                Supplier Selection Criterion: Other Terms of Delivery  ‐0.113  0.056  ‐0.107  ‐2.013 0.045                Supplier Selection Criterion: Product Quality  0.078  0.094  0.043   0.831  0.406                Supplier Selection Criterion: Reference     0.040  0.054     0.039   0.741  0.460                Supplier Selection Criterion: CSR Compatibility  0.040  0.044  0.050  0.910  0.363","Castek_1_Castek  23.1.2015  7:38  Stránka 129                                                                                                   129                                  6 Interpretation of the results achieved                          This chapter focuses on the characteristics of the sample and its individual subgroups                   depending on the selected variables. There are 10 variables that were selected on the                   basis of the application of the DAF 74 method as factors that have the greatest impact                   on the financial performance of companies. These variables were supplemented by an                   additional 6 variables with regard to the interpretation needs. The order of these                   sixteen variables was adjusted with respect to the logic of interpretation. They are                   listed in the Table 6-44                       As mentioned in Chapter 2, the sample of companies analysed was evaluated using                   the summation of two indicators, i.e. ROA and Assets Growth. Out of the 432 companies                   for which data were obtained from the questionnaire survey, 408 could be evaluated,                   while the remaining 24 had insufficient data. We consider this set of 408 companies                   a sample for the needs of this chapter. These businesses were ranked using the sum value                   of the indicators, ranging from companies with the highest value, i.e. businesses with                   the highest financial performance, to companies with the lowest financial performance.                   The sample was then divided into quartiles comprising 102 companies each. In the                   following text, these quartiles are indicated as a group of companies A, B, C and D.                   Companies with the highest financial performance are in group A, while companies                   with the lowest financial performance are included in group D.","Castek_1_Castek  23.1.2015  7:38  Stránka 130                  130  6 INTERPRETATION OF THE RESULTS ACHIEVED                     Table 6-44: Overview of variables                              Variable                         Note                  Variable type                    P Industry            1= manufacturing, 2 = construction industry  nominal                     P Legal form          1 = Ltd., 2 = joint‐stock company       nominal                     P Company size        1 = 50‐99, 2 = 100‐249, 3 = 250 or more employees  ordinal                     P Concern             1 = no, 2 = yes                         dichotomous                     F4 FDI                1= without foreign capital, 2 = with foreign capital  nominal                                          1=the only owner, 2=majority owner, 3=several big                    P Ownership concentration                                     nominal                                          owners                                          1 = cost leadership, 2 = differentiation, 3 = cost                    F1 Strategy                                                   nominal                                          focus, 4 = differentiation focus                    F5 Share of exports   the share of exports on sales (%)       interval                    F6 Span of control    an average number of employees per manager (%)  interval                                           the ratio of the average upper limit of the motivation                    F2 Motivation of workers                                      interval                                          component of workers’ wage to their base wage (%)                                          the ratio of the average upper limit of the motivation                    F3 Motivation of top                                          component of top managers’ salary to their base  interval                    management                                          salary (%)                    F8 Ratio of technical   the ratio of technical and administrative staff to the                                                                                  interval                    and administrative staff  total number (%)                    F9 Ratio of workers   the ratio of workers to the total number of staff (%)  interval                    F7 Ratio of women     the ratio of women to the total number of staff (%)  interval                    F10 Reasons for staff   1=  less than 2%, 2 = 2‐10%,  3 = more than 10%  ordinal                    urnover rate                                          1= low (obsolete machinery), 2, 3, 4, 5 = high (top‐of‐                    P Assets level                                                ordinal                                          the‐range machinery)","Castek_1_Castek  23.1.2015  7:38  Stránka 131                                                            6.1 OVERALL CHARACTERISTICS OF THE SAMPLE  131                     6.1 Overall characteristics of the sample                     In this section, the characteristics of the sample as a whole is described partially, i.e.                   according to each of the sixteen variables mentioned above; moreover, groups A, B, C                   and D are described within the sample.                     Industry                    The data were obtained from 408 companies, i.e. 100% of the sample.                       Companies from the manufacturing industry represent 80.4% of the sample,                   while companies from the construction industry account for 19.6% of the sample.                       As shown in Graph 6-3, companies from the construction industry show a                   significantly higher financial performance than companies from the manufacturing                   industry.                       Out of the total number of manufacturing companies, 22.9% of them belong to                   group A, 23.2% to group B, 27.4% to group C and 26.5% to group D.                       Out of the total number of construction companies, 33.8% of them belong to                   group A, 32.5% to group B, 15.0% to group C and 18.8% to group D.                       In other words: the percentage of manufacturing companies that are included in the                   two top quartiles, i.e. in groups A and B, is only about 46% of their total number. On the                   other hand, the percentage of construction companies included in groups A and B                   exceeds 66%.                    Graph 6-3: Relative frequency of quartiles in manufacturing and construction                                    Legal form                     The data were obtained for 408 companies, i.e. 100% of the sample.                       The sample includes 55.4% of private limited companies and 44.6% of joint-stock                   companies.                       As shown in Graph 6-4, private limited companies show a significantly higher                   financial performance than joint-stock companies.","Castek_1_Castek  23.1.2015  7:38  Stránka 132                  132  6 INTERPRETATION OF THE RESULTS ACHIEVED                         Out of the total number of private limited companies whose financial                   performance was analysed, 31.0% of them belong to group A, 27.4% to group B, 20.4%                   to group C and 21.2% to group D.                       Out of the total number of joint-stock companies, 17.6% of them belong to group                   A, 22.0% to group B, 30.8% to group C and 29.7% to group D.                       In other words: the percentage of private limited companies that are included in                   the two top quartiles, i.e. in groups A and B, exceeds 58% of their total number. On                   the other hand, the percentage of joint-stock companies included in groups A and B                   accounts for less than 40%.                     Graph 6-4: Relative frequencies of quartiles in private limited companies and in joint stock companies                                       Company size                     The data were obtained from 408 companies, i.e. 100% of the sample.                       The sample includes 29.2% of small companies with 50 to 99 employees, 41.7%                   of medium-sized companies with 100 to 249 employees, and 29.2% of large companies                   with at least 250 employees.                       As shown in Graph 6-5, smaller companies show a higher financial performance                   than larger ones.                       Out of the total number of companies with 50 to 99 employees, 29.4% of them                   belong to group A, 28.6% to group B, 18.5% to group C and 23.5% to group D.                       Out of the total number of companies with 100 to 249 employees, 27.1% of them                   belong to group A, 20.6% to group B, 24.7% to group C and 27.6% to group D.                       Out of the total number of companies with at least 250 employees, 17.6% of them                   belong to group A, 27.7% to group B, 31.9% to group C and 22.7% to group D.                       The percentage of small businesses, which are included in the two top quartiles,                   i.e. in groups A and B, accounts for 58% of the total number, while the percentage of                   medium-sized companies is less than 48%, and the percentage of large companies is                   only about 45%.","Castek_1_Castek  23.1.2015  7:38  Stránka 133                                                            6.1 OVERALL CHARACTERISTICS OF THE SAMPLE  133                     Graph 6-5: Relative frequencies of quartiles according to company size                                           Concern                    The data were obtained from 401 companies, i.e. 98.3% of the sample.                       The percentage of companies from the sample that belong to a concern is less                   than a third – namely 28.7% – while companies that are not part of a concern represent                   71.3% of the sample.                       As shown in Graph 6-6, companies that belong to a concern show a slightly higher                   financial performance.                       Out of the total number of companies that are part of a concern, 25.2% of them                   belong to group A, 29.6% to group B, 27.8% to group C and 17.4% to group D.                       Out of the total number of companies that are not part of a concern, 25.2% of                   them belong to group A, 22.7% to group B, 24.1% to group C and 28.0% to group D.                       The percentage of businesses belonging to a concern, which are included in the                   two top quartiles, i.e. in groups A and B, accounts for almost 55% of the total number;                   on the other hand, the percentage of companies from groups A and B that are not part                   of a concern is less than 48%.                    Graph 6-6: Relative frequencies of quartiles according to concern membership","Castek_1_Castek  23.1.2015  7:38  Stránka 134                  134  6 INTERPRETATION OF THE RESULTS ACHIEVED                     FDI                    The data were obtained from 347 companies, i.e. 85.0% of the sample.                       72.2% of companies from the sample are owned locally while in the remaining                   27.4% of companies foreign capital is involved in their ownership; in most cases, these                   situations include big majority or even 100% ownership.                       As shown in Graph 6-7, there is almost no difference in financial performance                   between companies that are owned locally and companies with foreign owners.                       Out of the total number of companies that are owned only locally, 24.2% of them                   belong to group A, 26.6% to group B, 22.6% to group C and 26.6% to group D.                       Out of the total number of companies with foreign owners, 25.3% of them belong                   to group A, 26.3% to group B, 27.4% to group C and 21.1% to group D.                       The percentage of locally owned businesses, which are included in the two top                   quartiles, i.e. in groups A and B, accounts for approximately 51% of the total number, while                   the percentage of companies from groups A and B with foreign owners is about 52%.                    Graph 6-7: Relative frequencies of quartiles in companies with and without FDI                                     Ownership concentration                    The data were obtained from 395 companies, i.e. 96.8% of the sample.                       The sample includes 38.5% of companies with a single owner, 21.8% of companies                   with a majority owner and 39.7% of companies owned by several big owners.                       As shown in Graph 6-8, companies with several big owners show the highest                   financial performance while companies with a majority owner show the lowest                   financial performance.                       Out of the total number of companies with a single owner, 27.0% of them belong                   to group A, 23.0% to group B, 23.7% to group C and 26.3% to group D.                       Out of the total number of companies with a majority owner, only 18.6% of them                   belong to group A, 25.6% to group B, 29.1% to group C and 26.7% to group D.                       Out of the total number of companies owned by several big owners, 26.1% of                   them belong to group A, 27.4% to group B, 22.9% to group C and 23.6% to group D.","Castek_1_Castek  23.1.2015  7:38  Stránka 135                                                            6.1 OVERALL CHARACTERISTICS OF THE SAMPLE  135                         The percentage of companies with a single owner that are included in the two top                   quartiles, i.e. in groups A and B, accounts for 50% of their total number; the percentage                   of companies with a majority owner included in groups A and B accounts for only                   about 44%. On the other hand, the percentage of companies owned by several big                   owners included in groups A and B exceeds 53%.                    Graph 6-8: Relative frequencies of quartiles according to the ownership concentration                                         Strategy                   The data were obtained from 351 companies, i.e. 86.0% of the sample.                       The sample includes 23.1% of companies using the cost-leadership strategy, 29.3%                   of companies using the differentiation strategy, 18.8% of companies using the cost-                   focus strategy, and 28.8% of companies using the differentiation-focus strategy.                       As shown in Graph 6-9, an association between an applied strategy and financial                   performance is very weak. Yet, there is some effect of strategy: companies using the                   differentiation strategy show lower financial performance. As for the companies using                   one of the three remaining strategies, their financial performance is higher and they                   do not differ very much.                       Out of the total number of companies using the cost-leadership strategy, 18.5% of                   them belong to group A, 33.3% to group B, 17.3% to group C and 30.9% to group D.                       Out of the total number of companies using the differentiation strategy, 24.3% of                   them belong to group A, 20.4% to group B, 26.2% to group C and 29.1% to group D.                       Out of the total number of companies using the cost-focus strategy, 28.8% of                   them belong to group A, 24.2% to group B, 19.7% to group C and 27.3% to group D.                       Out of the total number of companies using the differentiation-focus strategy,                   28.7% of them belong to group A, 25.7% to group B, 27.7% to group C and 17.8% to                   group D.                       The percentage of companies using the cost-leadership strategy that are included                   in the two top quartiles, i.e. in groups A and B, accounts for almost 52% of their total","Castek_1_Castek  23.1.2015  7:38  Stránka 136                  136  6 INTERPRETATION OF THE RESULTS ACHIEVED                     Graph 6-9: Relative frequencies of quartiles according to generic strategy                                                  number. The percentage of companies using the differentiation strategy included in                   groups A and B accounts for less than 45%. The percentage of companies using the                   cost-focus strategy included in groups A and B accounts for 53%. Finally, the                   percentage of companies using the differentiation-focus strategy included in groups                   A and B accounts for approximately 54%.                    Share of exports                    The data were obtained from 376 companies, i.e. 92.2% of the sample.                       Companies with predominant exports represent a minority in the sample. The                   percentage of companies whose share of exports on sales is more than fifty per cent                   accounts for 34.3% in the sample. There are only 4% of companies that export all their                   production, while the percentage of companies that do not export at all is 23.6%.                       It should be pointed out that there are striking differences between the                   manufacturing industry and construction: in the manufacturing industry, the                   percentage of companies with more than a 50% export share on sales is 43.1% of their                   total number, there are no such companies in the construction industry. The largest                   share of exports on sales is 30% here and only three companies show this figure.                       It appears that the export orientation of companies is generally in opposition to                   their financial performance. As shown in Graph 6-10, group A includes only 30.3%                   of companies with more than a 50% share of exports on sales, group B includes 34.0%                   export-oriented companies, in group C their representation is highest – 40.9%, and                   group D includes 36.1% of such companies.","Castek_1_Castek  23.1.2015  7:38  Stránka 137                                                            6.1 OVERALL CHARACTERISTICS OF THE SAMPLE  137                     Graph 6-10: Share of companies with predominant exports in the quartiles                                             Span of control                    The data were obtained from 393 companies, i.e. 96.3% of the sample.                       The average number of employees who report to one manager in a company is                   13.1 for all companies from the sample.                       The average number of employees who report to one manager in a company is                   12.5 for all companies from group A, 15.0 for companies from group B, 12.2 for                   companies from group C and 13.1 for companies from group D.                    Graph 6-11: The average span of control in the quartiles","Castek_1_Castek  23.1.2015  7:38  Stránka 138                  138  6 INTERPRETATION OF THE RESULTS ACHIEVED                         We can conclude that there is no zero-order relationship between the span of                   control and financial performance.                    Motivation of workers                     The data were obtained from 345 companies, i.e. 84.6% of the sample.                       The average upper limit of the motivation components of workers’ wages is 26.7%                   of the basic wage for all companies from the sample.                       The results shown in Graph 6-12 imply a certain, though very weak correlation:                   companies with a higher motivation component of workers’ wages tend to be the                   companies with higher financial performance.                       The average upper limit of the motivation components of workers’ wages is 28.7%                   of the basic wage in companies from group A, 26.2% in companies from group B,                   26.3% in companies from group C and 25.2% in companies from group D.                    Graph 6-12: The average upper limit of the motivation components of workers` wages in the quartiles                                             Motivation of top management                    The data were obtained from 345 companies, i.e. 84.6% of the sample.                       The average upper limit of the motivation components of top-managers’ salaries                   is 34.4% of the basic salary for all companies from the sample.                       The average upper limit of the motivation components of top-managers’ salaries                   is 35.9% of the basic salary in companies from group A, 31.2% in companies from                   group B, 39.5% in companies from group C and 33.0% in companies from group D.                       We can conclude that there is no zero-order relationship between the motivation                   component of the salaries and financial performance.","Castek_1_Castek  23.1.2015  7:38  Stránka 139                                                            6.1 OVERALL CHARACTERISTICS OF THE SAMPLE  139                     Graph 6-13: The average upper limit of the motivation components of top-managers’ salaries in the                   quartiles                                            Ratio of technical and administrative staff                     The data were obtained from 394 companies, i.e. 96.6% of the sample.                       The average percentage of technical and administrative staff from the total                   number of employees is 28.7% for all companies from the sample.                       Using the perspective of a particular industry, the average percentage of technical                   and administrative staff is lower (28.0%) in manufacturing companies than in                   construction ones (31.6%).                    Graph 6-14: The average percentage of technical and administrative staff in the quartiles","Castek_1_Castek  23.1.2015  7:38  Stránka 140                  140  6 INTERPRETATION OF THE RESULTS ACHIEVED                         The results shown in Graph 6-14 imply a certain, though very weak correlation:                   companies with a higher ratio of technical and administrative staff tend to be the                   companies with higher financial performance.                       The average percentage of technical and administrative staff is 32.9% in                   companies from group A, 27.8% in companies from group B, 29.2% in companies                   from group C and 25.6% in companies from group D.                   Ratio of workers                    The data were obtained from 394 companies, i.e. 96.6% of the sample.                       The average percentage of workers from the total number of employees is 71.3%                   for all companies from the sample.                       The results shown in Graph 6-15 imply a certain, though very weak correlation:                   companies with a lower ratio of workers tend to be the companies with higher                   financial performance.                       The average percentage of workers is 67.1% in companies from group A, 72.2%                   in companies from group B, 70.8% in companies from group C and 74.4% in                   companies from group D.                    Graph 6-15: The average percentage of workers in the quartiles                                             Ratio of women                    The data were obtained from 390 companies, i.e. 95.6% of the sample.                       The average percentage of women from the total number of employees is 26.9%                   for all companies from the sample.                       The results showed in Graph 6-16 suggest that companies with a lower ratio of                   women tend to be the companies with higher financial performance.","Castek_1_Castek  23.1.2015  7:38  Stránka 141                                                            6.1 OVERALL CHARACTERISTICS OF THE SAMPLE  141                         The average percentage of women is 21.5% in companies from group A, 26.1%                   in companies from group B, 27.2% in companies from group C and 32.8% in                   companies from group D.                   Graph 6-16: The average percentage of women in the quartiles                                            Reasons for the staff turnover rate                    The data were obtained from 375 companies, i.e. 91.9% of the sample.                       The average frequency of reasons for the staff turnover rate (from the employee`s                   initiative) is 1.73 points for all companies from the sample.                     Graph 6-17: The average frequency of reasons for the staff turnover rate (from the employee`s                   initiative) in the quartiles","Castek_1_Castek  23.1.2015  7:38  Stránka 142                  142  6 INTERPRETATION OF THE RESULTS ACHIEVED                         The results showed in Graph 6-17 suggest that there is a lower frequency of                   reasons for the staff turnover rate (from the employee`s initiative) in companies with                   higher financial performance.                       The average frequency of reasons for the staff turnover rate (from the employee`s                   initiative) is 1.68 points in companies from group A, 1.70 points in companies from                   group B, 1.73 points in companies from group C and 1.78 points in companies from                   group D.                     Assets level                    The data were obtained from 400 companies, i.e. 98.0% of the sample.                       The average tangible assets level is 3.54 points for all companies from the sample.                       The results in Graph 6-18 suggest that companies with a higher tangible assets                   level show higher financial performance.                       The average tangible assets level is 3.84 points in companies from group A, 3.58                   points in companies from group B, 3.54 points in companies from group C and 3.22                   points in companies from group D.                    Graph 6-18: The average tangible assets level in the quartiles","Castek_1_Castek  23.1.2015  7:38  Stránka 143                                   6.2 IDENTIFICATION OF TYPICAL COMBINATIONS OF FACTOR VALUES LEADING ...  143                     6.2 Identification of typical combinations of factor values                        leading to certain types of financial performance                      As we mentioned in the previous chapter, the entire sample of companies analysed                   was divided according to their financial performance into four quartiles containing                   102 companies each, labelled as either group A, B, C or D. In the subsequent                   considerations, we assume that the financial performance typical for each group can                   be achieved in several ways, i.e. combining different values of those variables that                   crucially affect the financial performance of companies. In order to identify these                   typical combinations, businesses in each of the groups A, B, C and D were subjected                   to a cluster analysis, performed using sixteen of the above-mentioned variables.                       While respecting the reasonable range of the text, we focus only on one of the                   groups when presenting the interpretation of the obtained results. With regard to the                   principle of “best practices”, we chose group A. We want to use it to demonstrate what                   different combinations of variable values (characteristics) lead to high financial                   performance of a company.                       First, in relation to the previous subchapter, we characterize group A as a whole,                   then the individual subgroups A 1 to A 5, which result from the application of the                   cluster analysis.                     Group A as a whole                    Group A shows a relatively high proportion of companies from the construction                   industry. Out of their total number in the sample, nearly 34% of them belong here,                   while the proportion of companies from the manufacturing industry is only less than                   23% of their total number.                       Limited liability companies also have a relatively higher representation in this                   group. Out of their total number, 31% of them are represented in this group, while the                   proportion of joint-stock companies is less than 18% of their total number in group A.                       Companies with 50–99 employees have the relatively highest representation in                   group A: out of their total number more than 29% of businesses belong here. In the                   case of companies with 100–249 employees, about 27% from their total number                   belong here. As for companies with at least 250 employees, less than 18% belong to                   group A.                       The representation of companies in group A does not differ depending on                   whether a company is or is not part of a concern. In both cases the percentage is the                   same and amounts to slightly more than 25%.                       The representation of companies depending on whether they are owned locally                   or by a foreign owner is very similar. Out of the total number of businesses that are                   owned only locally, approximately 24% belong to group A, while a little more than                   25% of companies that are partly or fully owned by a foreign owner belong here.","Castek_1_Castek  23.1.2015  7:38  Stránka 144                  144  6 INTERPRETATION OF THE RESULTS ACHIEVED                         However, after assessing the ownership structure more comprehensively, the                   relationships sought turn out to be clearer. In group A, two types have the largest                   relative proportion, namely:                   a)  companies that have a single owner and are part of a concern (75% of the total                       number of companies that are part of a concern),                   b) companies that have several large owners and are not part of a concern (almost                       56% of the total number of enterprises that are not part of a concern).                       These two types of ownership structure are present in nearly 60% of the                   companies included in group A.                       In group A there are relatively more frequently companies exercising the cost                   focus and differentiation focus strategies. In the case of cost focus, this group makes                   up nearly 29% of the total number of companies from the sample that exercise this                   strategy; in the case of differentiation focus, the figure is also almost 29%. On the                   contrary, companies using the cost leadership and differentiation strategies achieve                   lower financial performance on average. As for cost leadership, group A contains less                   than 19% of the total number of businesses applying this strategy, while in the case of                   differentiation, it is about 24%.                       The dominant strategies of cost focus and differentiation focus are closely related                   with a strong concentration on specific products. Of the total number of companies                   in group A, 71% has a prevailing focus on specific products.                       Companies in group A are characterized by low export orientation, which is                   somewhat surprising. As for group A, the representation of companies in which the                   share of exports in sales is predominant, i.e. higher than 50%, is the lowest compared                   with the other three groups (B, C and D). Only 30% of the companies from group A                   have a predominant share of exports in sales, i.e. they supply more products on the                   foreign market than the domestic one. This situation could be explained by the fact                   that in the period analysed there was a long-term appreciation of the domestic                   currency against the euro and the dollar. A certain influence can also be attributed to                   the relatively high representation of companies from the construction industry, whose                   exports are limited for technical reasons, typical for this sector. The construction                   companies from the sample do not contain a single business whose share of exports                   in sales would exceed the 50% threshold.                       The value of span of control is 12.5 for businesses from group A. It is almost equal                   to the value valid for group C and it is lower than in the other two groups.                       Systems of motivation in companies from group A provide a relatively large space                   for the motivational wage component both for workers – nearly 29% in average – and                   top management – almost 36% in average. In other words, according to the wage                   regulations, the upper limit of workers’ wages is on average about 1.29 times the base                   salary; in the case of top management, it is 1.36 times the base salary.                       Businesses represented in group A have – in comparison with those in groups B,                   C and D – a relatively higher proportion of technical and administrative staff of the                   total number of employees (almost 33%). It can be assumed that this situation is","Castek_1_Castek  23.1.2015  7:38  Stránka 145                                   6.2 IDENTIFICATION OF TYPICAL COMBINATIONS OF FACTOR VALUES LEADING ...  145                     related to the specificity of products, the predominant focus on differentiation                   strategies, and consequently to the higher proportion of intellectual work (research,                   development, marketing, and management). The second option may be relatively high                   labour productivity in manufacturing, caused by the fact that blue-collar occupations                   are largely equipped with technology.                       Companies from group A show a relatively low proportion of women in the total                   workforce. The fact that the figure is on average less than 22% can be explained by a                   relatively high proportion of construction companies in group A, where the                   employment of women is low. Similar reasons can be seen also in the structure of the                   categories in the manufacturing industry, where companies operating in the fields                   traditionally dominated by women, such as textile manufacturing, food production,                   etc., are included only to a limited extent.                       Compared with the other groups (B, C and D), companies in group A show the                   relatively lowest staff turnover initiated by employees. It amounts to 1.68 points on a                   three-point scale (1 – lowest to 3 – highest). This is undoubtedly related to the excellent                   economic results of companies in group A and the consequent pay conditions.                       The level of the significant components of tangible assets amounts to the value of                   3.84 points on a five-point scale (1 – lowest to 5 – highest) in companies from group                   A, and it is the highest compared with the other three groups. This suggests an                   influence of this factor on the financial performance of the companies analysed.                       Now, let us focus our attention in more detail on the particular groups of A 1 to A 5.                    Group A 1                    It includes 15 companies.                       They all belong to the manufacturing industry.                       This group includes 60% of private limited companies and 40% of joint-stock                   companies.                       All size categories are represented: small companies (50-99 employees), accounting                   for approximately 47%, medium-sized companies (100-249 employees), accounting for                   20%, and large companies (at least 250 employees) with a share of about 33%.                       Most companies (about 73%) are not part of a concern.                       About half of the companies in this group are owned by local owners, while the                   other half is partly or fully owned by foreign owners.                       As for the business strategies, the vast majority of these businesses implement                   strategies aimed at low cost (cost leadership and cost focus). These companies account                   for about 73% in group A 1.                       Only a small proportion of companies from group A 1 (about 15%) is export-                   oriented, i.e. their share of exports in sales is higher than 50%. The average share of                   exports in sales in a company amounts to approximately 33%.                       The span of control varies significantly from about four to almost twenty-two in                   the individual companies.","Castek_1_Castek  23.1.2015  7:38  Stránka 146                  146  6 INTERPRETATION OF THE RESULTS ACHIEVED                         In companies from group A 1, the average motivation component of workers’                   wages is almost 20%, which is less than the average for the whole group A (about 29%).                   Similar findings hold for the average motivation component of top management                   salaries. The share of this component is about 32% in companies from group A 1,                   while the average for the whole group A is nearly 36%.                       The ratio of technical and administrative staff to the total number of employees                   differs substantially for each company. On average it reaches nearly 37% and it is higher                   than the average of group A (about 33%) as well as the entire sample (less than 29%).                       Considerably volatile values are also observed for the indicator ratio of workers                   to the total number of employees. The nature of the calculation shows that it is                   complementary to the previous indicator: on average it amounts to about 63% and it                   is lower than the average of group A (approximately 67%) as well as the entire sample                   (about 71%).                       The ratio of women to the total number of employees is very high in the                   individual companies from group A 1. It ranges from 33% to 80%, and the average                   reaches to almost 55% of the total number of company employees. It is significantly                   higher than the average for the whole group A (about 22%) as well as the entire sample                   (27%). Industry specifics seem to have the main effect: the highest ratio of women (75                   to 80%) occurs here in four companies, operating in the field of baking, toy                   manufacturing, textile production, and book publishing.                       Staff turnover initiated by employees, measured on a scoring scale of 1 – lowest                   to 3 – highest, reaches the average value of 1.73 points. It is equal to the average value                   of the entire sample and it is higher than the average value for the whole group A                   (1.68).                       The level of the significant components of tangible assets, measured on a scoring                   scale of 1 – lowest to 5 – highest, reaches the average value of 3.67 points. It is lower than                   the average value in group A (3.84), but higher than the value of the entire sample (3.54).                    Group A 2                    It includes 28 companies.                       They all belong to the manufacturing industry.                       In terms of the legal form of business, group A 2 contains significantly more                   private limited companies. There are 20 of them; thus, their proportion is more than                   71%. The rest are joint-stock companies.                       Size categories are represented equally: small companies (50-99 employees) with a                   share of about 32%, medium-sized companies (100-249 employees), accounting for                   approximately 36%, and large companies (at least 250 employees) with a share of about                   32%.                       The share of companies that are not part of a concern is higher, but not                   significantly. There are 16 companies (more than 57%) compared with 12 companies                   (less than 43%) that are part of a concern.","Castek_1_Castek  23.1.2015  7:38  Stránka 147                                   6.2 IDENTIFICATION OF TYPICAL COMBINATIONS OF FACTOR VALUES LEADING ...  147                         Local owners own approximately two-thirds of companies from this group, and                   one-third is fully or partly owned by foreign owners. Foreign owners own almost all                   the businesses that are part of a concern.                       Businesses in group A 2 predominantly apply strategies aimed at the specific                   nature of their products with the option to demand higher prices. Application of                   strategies aimed at low cost is rare. Specifically: of the twenty-six companies (two did                   not provide information), 16 (i.e. approximately 62.5%) pursue the strategy of                   differentiation focus, and 3 companies (approximately 11.5%) apply the differentiation                   strategy. In contrast, 6 companies apply the cost focus strategy (about 23%) and only                   one company (less than 4%) applies the cost leadership strategy.                       Group A 2 is typical for its exceptionally high export orientation. The average                   share of exports in sales is nearly 85% for businesses in this group. All 23 companies                   that answered this question report an at least 50% share of exports in sales. Of these                   companies, 12 report that their export share is 90% or more; 4 of these businesses                   export their entire production.                       Similarly to the previous group, the span of control is very volatile in these                   companies, ranging from about three to almost twenty-seven.                       In companies from group A 2, the average motivation component of workers’                   wages is almost 24%. This is less than the average for group A as a whole                   (approximately 29%) and also less than the average of the sample (nearly 27%). Similar                   findings also hold for the average motivation component of top management salaries.                   The share of this component is about 29% in companies from group A 2, while the                   average for the whole group A is almost 36% and the average for the entire sample is                   about 34%.                       Similarly to the previous group, even here the ratio of technical and                   administrative staff and the ratio of workers to the total number of employees in each                   company differ substantially. On average, the ratio of technical and administrative                   staff is higher than 31%. This value is lower than the average of group A (about 33%),                   but higher than the average of the entire sample (less than 29%). The nature of the                   calculation shows that the ratio of workers is complementary to the previous indicator                   and it amounts to about 69% for companies in group A 2. It is higher than the average                   of group A (approximately 67%), but lower than the average of the entire sample                   (about 71%). A more detailed analysis shows that companies that are part of a concern                   have a smaller share of technical and administrative staff than companies that are not                   part of a concern. This is undoubtedly related to the centralization within the concern                   when a number of administrative, technical, or other similar activities that enterprises                   not included in a concern must perform themselves, are performed by the                   headquarters or a specialized organization for the concern units.                       The average ratio of women to the total number of employees is about 25% in the                   companies from group A 2. This value is significantly lower than the average value                   for the companies in group A 1 (nearly 55%). However, it is higher than the average                   for the whole group A (about 20%), but slightly lower than the average of the entire","Castek_1_Castek  23.1.2015  7:38  Stránka 148                  148  6 INTERPRETATION OF THE RESULTS ACHIEVED                     sample (27%). The highest ratio of women (80%) was found in a company engaged in                   the production of textiles.                       Staff turnover initiated by employees, measured on a scoring scale of 1 – lowest                   to 3 – highest, reaches an average of 1.7 points. It is higher than the average for the                   whole group A (1.68), but lower than the average value of the entire sample (1.73).                       The level of the significant components of tangible assets, measured on a scoring                   scale of 1 – lowest to 5 – highest, reaches an average value of 4.11 points. It is the                   highest value in group A as well as in the remaining three groups B, C and D. For the                   sake of comparison, the average value of the companies in group A is 3.84 points,                   while the average value of the entire sample is 3.54 points. Upon closer analysis we                   find that the average value of the level of tangible assets in companies that are part of                   a concern is 4.16 points. It can be assumed that this is due to inflows of investment                   from the concerns’ headquarters.                    Group A 3                     It includes only three companies.                       They all belong to the manufacturing industry and related categories: two belong                   to category 28 – Manufacture of metal constructions and fabricated metal products,                   and one to category 29 – Manufacture and reconstruction of machinery and                   equipment.                       In terms of their legal forms of business, they are private limited companies.                       One of the companies belongs to the size group of 50 to 99 employees and two                   companies belong to the size group of 100-249 employees.                       The smaller company is not part of a concern and it is owned by a local owner,                   while both larger businesses are part of a concern and they have foreign owners.                       The companies mainly apply strategies focused on the specific nature of their                   products, with the possibility of achieving higher prices (differentiation and                   differentiation focus strategies).                       All the businesses have a strong export orientation. The share of exports in sales                   amounts to 70% for one of the companies and 95% for the two remaining companies.                       The span of control is clearly higher (16.8) for the company that is not part of a                   concern than for the companies that are part of a concern (7.48 and 9.92).                       The ratio of technical and administrative staff amounts to 16%, 23% and 24% in                   these companies. The values are significantly lower than the average of group A (about                   33%), and the average of the entire sample (less than 29%).                       The ratio of women to the total number of employees is low, which is undoubtedly                   caused by the industry focus (manufacture of fabricated metal products). In one of the                   companies it is only 5%, while in the remaining two companies it is about 13% and 15%.                       Staff turnover initiated by employees, measured on a scoring scale of 1 – lowest                   to 3 – highest, which amounts to 1.4, 1.2 and 2.2 points in the individual companies,                   can be considered average, on the whole.","Castek_1_Castek  23.1.2015  7:38  Stránka 149                                   6.2 IDENTIFICATION OF TYPICAL COMBINATIONS OF FACTOR VALUES LEADING ...  149                         The level of the significant components of tangible assets, measured on a scoring                   scale of 1 – lowest to 5 – highest, reaches an average value of 3 points. It is lower than                   both the average value in group A (3.84) and the average value of the entire sample (3.54).                    Group A 4                    It includes 43 companies.                       While in the previous three groups, there were no businesses from the                   construction industry, there are many of them in this group. The number of                   construction companies is 23, which represents 27.7% of their total number in the                   sample (83) of. There are 20 companies from the manufacturing industry, but this                   represents only 5.7% of the total number of these companies in the sample (349).                       In terms of the legal form of business, this group includes 27 private limited                   companies and 16 joint-stock companies.                       These businesses are mainly small and medium-sized companies. The group                   includes 15 companies from the category of 50 to 99 employees (about 35%), 22                   companies from the category of 100 to 249 employees (about 51%), and only 6                   companies with at least 250 employees (14%).                       The share of companies that are part of a concern is not big: there are 10                   companies of this type from the total number of 43 companies included in this group,                   i.e. about 23%.                       Only a few enterprises (6) are owned by foreign owners. These are the businesses                   that are part of a concern.                       As in the case of companies from groups A 2 and A 3, the strategies of companies                   in this group focus on the specific nature of their products with the possibility to demand                   higher prices rather than on achieving low cost. However, compared with the previous                   two groups, this orientation is slightly less significant in group A 4. 14 companies (i.e.                   about 35.9%) of 39 (4 did not respond) pursue the differentiation strategy while 10                   companies (about 25.6%) follow the differentiation focus strategy. In contrast, the                   strategy of cost leadership is followed by 8 companies (approximately 20.5%) and 7                   companies (about 17.9%) implement the strategy of cost focus. If we compare this                   strategic orientation in manufacturing and construction companies, we find that this                   orientation is more significant in the construction industry. While approximately 61.5%                   of the total number of companies in group A 4 pursue the strategies of differentiation                   and differentiation focus, the percentage of manufacturing companies applying these                   strategies is less than 59%; on the other hand, the percentage of construction companies                   amounts to nearly 64%. This fact can be attributed to industry specificities.                       Export orientation of companies in group A 4 is very low; more than half of the                   businesses do not export at all. Of the 40 companies that answered the respective                   question, there are only 9 (i.e. 22.5%) whose share of exports in sales is 10% or more.                   The maximum export share is 40% and it is reported by one company. “Non-export”                   orientation is significant especially for construction companies, which is typical for","Castek_1_Castek  23.1.2015  7:38  Stránka 150                  150  6 INTERPRETATION OF THE RESULTS ACHIEVED                     the construction industry. Zero export is reported by 16 of the 23 construction                   companies. In contrast, there are only two construction companies whose share of                   exports in sales amounts to 10% or more.                       The span of control is very volatile in the individual businesses, even more than                   in groups A 1 and A 2. It can be said that it has virtually no explanatory value as a                   characteristics of the companies from this group.                       The average motivation component of workers’ wages is lower than 25% in the                   companies of group A 4. This is less than the average for the whole group A                   (approximately 29%) and also less than the average of the sample (nearly 27%). Similar                   figures are found even for the average motivation component of top management salaries.                   In companies from group A 4, the share of this component is less than 33%, while the                   average for the whole group A is almost 36% and for the entire sample it is about 34%.                       Similarly to the previous groups, even here the ratio of technical and                   administrative staff and the ratio of workers to the total number of employees differ                   substantially in the individual companies; on average, they reach more than 36%. This                   value is higher than the average for group A (about 33%) and significantly higher than                   the average for the entire sample (less than 29%). Eight companies from the total                   number of 42 in group A reported that their ratio of technical and administrative staff                   is 50% and higher; three of these businesses are manufacturing companies and five                   are construction companies. In addition to their production activities, these                   companies are to a large extent engaged in engineering and design activities.                       Businesses in group A 4 have on average a low ratio of women to the total                   workforce; the value is about 13%. This value is lower than the average for the whole                   group A (about 22%), and significantly lower than the average for the entire sample                   (27%). It is interesting that there is no big difference between the manufacturing and                   construction companies. The average ratio of women is about 14% in the                   manufacturing companies and about 12% in the construction companies. A company                   engaged in the production of computers and medical devices reported the highest                   ratio of women, reaching the value of 43%.                       Staff turnover initiated by employees, measured on a scoring scale of 1 – lowest                   to 3 – highest, reaches an average value of 1.66 points. Is approximately the same as                   the average value for the whole group A (1.68), but lower than the average value for                   the entire sample (1.73).                       The level of the significant components of tangible assets, measured on a scoring                   scale of 1 – lowest to 5 – highest, reaches an average value of 3.81 points. This value is                   similar to the average for the whole group A (3.84). However, it is significantly higher                   than the average value for the entire sample (3.54).                   Group A 5                    It includes 13 companies.                       Similarly to the previous group of A 4, this group includes both manufacturing                   companies (9 businesses) and construction companies (4). It represents about 2.6%","Castek_1_Castek  23.1.2015  7:38  Stránka 151                                   6.2 IDENTIFICATION OF TYPICAL COMBINATIONS OF FACTOR VALUES LEADING ...  151                     of the total number of manufacturing companies in the sample and approximately                   4.8% of the total number of construction companies.                       With the exception of two businesses that are joint-stock companies, they are                   private limited companies (11 businesses).                       They are mostly medium-sized companies, i.e. they belong to the category of                   companies with 100 to 249 employees; their number in this group is 9 (about 70%).                   The number of small businesses, i.e. the category of companies with 50 to 99                   employees, is 3 (about 23%). There is only one large company (about 7%), whose                   number of employees is at least 250.                       Only one of the companies in this group is part of a concern. Most businesses are                   owned by local owners.                       The differentiation strategy is the most commonly applied business strategy; of                   the ten companies that responded to this question, six pursue it. As for the other                   strategies, two businesses apply the cost focus strategy and two businesses use the cost                   leadership strategy.                       Export orientation of the companies is low. Of the ten companies that responded                   to this question, 4 companies do not export at all, 3 of which belong to the                   construction industry. For the remaining six companies, the share of exports in sales                   is up to 50%.                       The number of workers who report to one superior in the businesses of group A                   5 is considerably volatile, like in the previous groups. It ranges from about five to about                   thirty-six. Nevertheless, the explanatory power of this indicator is problematic.                       The average motivation component of workers’ wages is extremely high in the                   businesses of group A 5 as it amounts to more than 55%. This is substantially more                   than the average for the whole group A (approximately 29%) as well as the average                   for the sample (nearly 27%). Similarly, the average motivation component of top                   management salaries is also extremely high. In companies from group A 5, the amount                   of this component is more than 68%, while the average for the whole group A is about                   36% and for the entire sample it is about 34%.                       The ratio of technical and administrative staff to the total workforce is not                   considerably volatile, as it was in the previous group; it amounts to 25% on average.                   This value is significantly lower than the average for group A (about 33%), and lower                   than the average for the entire sample (less than 29%).                       Similarly to the businesses in group A 4, the average ratio of women to the total                   number of company employees is also low in the companies from group A 5; the value                   is less than 13%. This value is lower than the average for the whole group A (about                   22%), and significantly lower than the average for the entire sample (27%). The ratio                   of women in construction companies is lower than it is in manufacturing companies                   as it ranges from 5 to 10%.                       Staff turnover initiated by employees, measured on a scoring scale of 1 – lowest to                   3 – highest, reaches an average value of 1.68 points. It is identical with the average for                   the whole group A (1.68), but lower than the average value for the entire sample (1.73).","Castek_1_Castek  23.1.2015  7:38  Stránka 152                  152  6 INTERPRETATION OF THE RESULTS ACHIEVED                         The level of the significant components of tangible assets, measured on a scoring                   scale of 1 – lowest to 5 – highest, reaches an average of 3.7 points. This value is lower                   than the average for the whole group A (3.84); however, it is higher than the average                   value for the entire sample (3.54).                      6.3 Summary                     Based on the conducted analysis and its subsequent interpretation, we will now focus                   on those variables that best describe the specifics of companies included in the above                   groups. They are listed in table 6-45 and table 6-46.                       In the following explanation to table 6-45 and table 6-46, we deal with only four                   of the five groups listed above, namely groups A 1, A 2, A 4 and A 5. Group A 3,                   containing only three businesses, will not be dealt with due to its insignificant size. It                   may be said, though, that this group is very close to group A 2 in terms of the variables                   that we are focusing on here.                       It is typical for group A 1 that it includes only businesses from the manufacturing                   industry. However, there is considerable branch heterogeneity within this industry.                       Compared with the other three groups, it has the highest share of businesses                   owned by foreign owners (46% of companies).                       Unlike in the other three groups, businesses in this group, very significantly prefer                   those strategies that are aimed at low cost (72% of companies).                       These are mainly domestic-market suppliers. The average share of exports in                   company sales amounts to 33%.                       The level of the significant components of tangible assets is slightly below average;                   compared with companies in the other three groups it is the lowest.                       It is also typical for group A 2that it includes only businesses from the manufacturing                   industry. Branch heterogeneity is slightly lower than in the case of group A 1.                       Compared with the other three groups, the share of businesses that are part of a                   concern owned by foreign investors is the highest here.                       Companies in this group typically pursue the differentiation-type strategies,                   namely the differentiation focus (62.5%) and differentiation (11.5%) strategies.                   Companies whose strategies are aimed at low cost represent a minority.                       Businesses in group A 2 have an extremely high export orientation. The average                   share of exports in company sales in this group amounts to as much as 85%.                       A high level of the significant components of tangible assets relates with the                   implementation of the differentiation-type strategies and the ability to succeed in                   foreign markets; this level is significantly higher than in the other three groups. It can                   be assumed that in many cases these are companies included in concerns that were                   equipped with high-quality machinery and equipment by their headquarters.                       Unlike groups A 1 and A 2, group A 4 includes construction companies as well                   as manufacturing companies.","Castek_1_Castek  23.1.2015  7:38  Stránka 153                                                                                     6.3 SUMMARY•• 153                             Whole Sample  %  N  80  328  20  80  73  252  27  95  29  115  71  286  42  147  58  204  Whole Sample  %  N  37  3.54                                                                                       %                               %   74  26  71  29  29   71  39  61           A        34   3.83                          A                                                                                 N                               N   75  27  60  25  29   72  34  54                                                                                 %                               %   69  31  75  25  8    92  40  60           A 5      20   3.70                          A 5                                                    N                     Table 6-45: Summary of frequencies of categorical variables in the sample, group A and its subgroups                                                                       Table 6-46: Summary of average values of chosen variables in the sample, group A and its subgroups                               N   9   4   6   2   1    11  4   6                                                                                 %                               %   47  53  83  17  23   77  38  62           A 4      5    3.81                          A 4                                                    N                               N   20  23  30  6   10   33  15  24                                                                                 %                               %   100  0  33  67  67   33  0   100          A 3      87   3.00                          A 3                                                    N                               N   3   0   1   2   2    1   0   2                                                                                 %                               %   100  0  64  36  43   57  27  73           A 2      85   4.11                          A 2                                                    N                               N   28  0   16  9   12   16  7   19                                                                                 %                               %   100  0  54  46  27   73  73  27           A 1      33   3.67                          A 1                                                    N                               N   15  0   7   6   4    11  8   3                                      Manufacturing  Construction  Without FDI  With FDI  Yes  No  Low Cost (CL+CF)  Differentiation  (DIF+DF)  Share on Sales (%)  ASSETS LEVEL 1 ‐ lowest, 5 ‐ highest                                            INDUSTRY  FDI  CONCERN  MEMBERSHIP  STRATEGY     EXPORT","Castek_1_Castek  23.1.2015  7:38  Stránka 154                  154  6 INTERPRETATION OF THE RESULTS ACHIEVED                         A large majority of the companies (83%) are owned by a local owner, which is                   the biggest share of all the groups analysed.                       The share of companies in the group that are part of a concern (23%) can be                   considered slightly below average.                       Companies tend to prefer the differentiation-type strategies. The differentiation                   focus strategy is applied by 35.9% of the companies, while the differentiation strategy                   is used by 25.6% of companies.                       In most cases the companies are domestic-market suppliers. The average share                   of exports in company sales is only 5% in this group. None of the exporting companies                   shows a higher share of exports in sales than 40%.                       The level of significant components of tangible assets is close to the average for                   the whole group A.                       Group A 5 also includes both manufacturing and construction companies.                       Most companies (75%) are owned by a local owner.                       With the exception of one company, the businesses in this group are not part of                   a concern.                       Slightly more than half of the companies implement the differentiation-type                   strategies while the remaining businesses focus on low-cost strategies.                       The companies tend to be domestic-market suppliers. The average share of                   exports in company sales in this group is 20%.                       The level of the significant components of tangible assets is lower than the average                   for the whole group A.                       The conducted analyses suggest that the characteristics of groups A 1 and A 2 are                   distinct and mutually very different. The business philosophy of most companies in                   group A 1 could be “Keeping costs low and using the know-how of foreign owners”.                   In contrast, the business philosophy for most businesses in group A 2 might be                   “Meeting the specific requirements of foreign customers. Focusing on quality,                   using high-quality machinery and equipment”.                       The characteristics of groups A 4 and A 5 are neither as distinct nor different.                   These groups are quite similar, and to some extent they can be located between groups                   A 1 and A 2. Their common business philosophy can be formulated as follows: “Using                   namely good knowledge and contacts in the domestic markets in business                   activities”.","Castek_1_Castek  23.1.2015  7:38  Stránka 155                                                                                                   155                                  7 Conclusion                          The experience stemming from the research conducted confirmed the justified                   assumption that the task has been nontrivial and the methodology examined for its                   solution rather ambitious. We focus on the following areas in the final recapitulation,                   including problems associated with their solution.                    a)  Input data                       Input data were obtained from two sources: financial statements published in the                   Albertina database, and questionnaires that the participating companies completed                   during the empirical investigation.                       Data from the financial statements can be considered relatively accurate.                   However, the term “relatively” refers to the fact that in some cases all the data in the                   respective time series were not available; moreover, even various inaccuracies and                   distortions which the accounting practice can never completely exclude could occur                   here. Principally, the character of the information was objective.                       Nevertheless, the situation was different for the data obtained from the                   questionnaires. Although the respondents were asked for objective information, such                   as the number of employees in each category, the ratio of each type of customers on                   sales, etc., it was clear that the data will be predominantly estimates, given the difficulty                   of obtaining or calculating such indicators. However, respondents were also asked in                   ways that anticipated response subjectivity, as it resulted directly from the questions                   asked. For instance, one of these questions was “What is the level of tangible assets of                   your business ?” and the answer was supposed to be recorded on a scale of 1 to 5,                   where “1” meant obsolete equipment and “5” state-of-the-art equipment. It was left                   up to the respondents how they would assess the equipment on the scale. Another                   important question concerned, for example, the business strategy applied by a                   company. Four strategies were characterized very briefly (Cost Leadership,                   Differentiation, Cost Focus and Differentiation Focus). It was left up to the                   respondents under which of these generic strategies they will subsume the strategy of                   their company.","Castek_1_Castek  23.1.2015  7:38  Stránka 156                  156  7 CONCLUSION                         It is obvious that in many cases the researchers had to rely on experience,                   qualifications and the respondents’ responsibility. However, it should also be noted                   that the answers to those questions that were of a subjective nature eventually                   produced nominal and ordinal variables; these variables proved to be more useful for                   further processing with statistical methods and for the final interpretation than the                   numeric figures in the form of interval variables.                    b) Preparation of variables for entering the process of identifying financial                       performance factors based on learning approaches                       Using a questionnaire, the researchers obtained data which were expected to                   describe the business in a complex way if possible. The questionnaire was prepared                   in previous research. On the one hand, it was a compromise between the complexity                   and detail of the data, and on the other hand, between acceptability of the                   questionnaire length in terms of its completion by respondents and the subsequent                   analysis of the data obtained.                       After determining what specific requirements the methods of feature selection                   from the field of statistical pattern recognition impose on the input variables, a                   substantial modification of the set of these variables started. The needed size of the                   so-called “training set” is a problem that occurs when using learning approaches, with                   respect to the dimensionality of the space of features, i.e. their number. In our                   particular case, the ratio is the number of observations that are available to the number                   of tested (or explanatory in the case of a regression model) variables. A frequently                   used rule of thumb says that this ratio should be at least 10:1. There are more                   sophisticated rules formulated for specific methods and for different uses of these                   methods; but even if we accept this general rule, it is true that if we wanted to use all                   of the almost 700 variables obtained from the questionnaires, it would be necessary                   to have questionnaires from at least 7,000 companies. In a situation where the                   population included less than half this number of companies, it was, of course, an                   impossible requirement. Therefore, within a series of experiments that were conducted                   during the research, repeated selection and in many cases also re-codification of the                   original variables was gradually used. This measure undoubtedly had a very positive                   impact on solving the given task.                    c)  Identification of financial performance factors through statistical methods                       The original idea was to look for factors of corporate performance without an a                   priori model. In literature we commonly read about bivariate tests of correlations                   between potential performance factors and performance. In this case, however, the                   correlations found tend to be rather weak, which reflects the reality where these factors                   do not act separately. Thus, effects that can occur only with the involvement of the                   influence of other factors, which may even have no direct influence on performance,                   are not taken into account. Although it is possible to use these bivariate tests for the                   search of conditional or partial correlations, it is feasible only for a small number of","Castek_1_Castek  23.1.2015  7:38  Stránka 157                                                                                     7 CONCLUSION  157                     input variables and/or when testing a priori notions about these relationships. Another                   option is to use multidimensional models, with the most common ones being multiple                   regression models (general linear models), path analysis or structural equation                   models. They already take into account the interaction of multiple variables and are                   able to test complex causal models. Nevertheless, they still require a precise a priori                   idea of the tested correlations. Therefore, most studies of corporate performance focus                   on a specific area of a business, such as HRM, IT, or ownership structure etc. Although                   this covers the complicated links within the explanatory variables and between the                   explanatory variables and the dependent variables, it is always only for this one area                   and not across the areas. However, even variables from an “adjacent” area may play a                   role in explaining the effects of another variable, which also occurred in the results of                   our research. Thus, we pursued an exploratory type of research investigating the                   characteristics of businesses from various areas without the pre-formulated way of                   their anticipated effect. This, however, led to a vast increase in the number of variables                   required to sufficiently describe each company, i.e. in the dimensionality of the                   problem solved. Without an a priori model, which would at least partially reduce the                   number of possible interactions between the input variables, it was impossible to solve                   such a task in its completeness using the above-mentioned methods. This was the                   cause of the need to use different methodology. Methods of feature selection from the                   field of statistical pattern recognition proved suitable.                       Feature selection methods typically consist of an optimization procedure and                   criterion of quality of the examined subset of features. The optimization procedure                   searches the space of the subsets gradually with respect to the criterion values                   evaluated on the previously investigated configurations. Criterial functions may be                   based on parametric models of data; however, they can also be defined without the                   need to include model assumptions. In our context, we primarily examined non-                   parametric modelling; in this case, the criterial function worked directly with the data                   in the data file instead of selecting a model explicitly. This was achieved by introducing                   a criterial function evaluating only the statistics of metric distances of samples above                   the currently evaluated subspace. The defined solution was on the borderline between                   the “nearest neighbour” methods and methods of kernel estimates, and it made it                   possible to elegantly solve the problem of occasionally missing values of some features.                       By applying the feature selection methods, we were able to reduce the input                   variables to those that could either assign a company into the correct performance                   group in the best way, or predict this performance best. The disadvantage of the                   process bringing the highest accuracy and stability of this prediction (combination of                   the DAF method and a non-linear regression model) was the absence of guidelines                   to interpret the variables selected in this way. While the correlation coefficient shows                   the direction of the effect, or a linear regression model offers an equation explaining                   the dependent variable, a non-linear regression model, which we used as a measure                   of prediction accuracy, provided no such global guideline. The nonlinear model                   offered higher accuracy thanks to the ability to capture context-dependent","Castek_1_Castek  23.1.2015  7:38  Stránka 158                  158  7 CONCLUSION                     relationships between the features, i.e. different in various parts of the space.                   Observation of local dependencies between the features did not allow easy                   generalization leading to global conclusions about the features; it turned out that the                   same features could often manifest themselves as significant, insignificant, or even                   counterproductive, always depending on other currently selected features.                    d) Economic interpretation                       Interpretation of variables selected as “most informative” or best predicting                   corporate performance became a separate subsequent step. It is clear from the nature                   of the task solved that the purpose of interpretation is not to quantify the individual                   locally-dependent characteristics of the variables, but a meaningful generalization of                   this information towards an easily interpretable result. It involves a description of the                   space of variables, which has the potential to further clarify the features or feature                   groups defined by variables of companies, and in particular their mutual relations.                       For this purpose, the companies were grouped into smaller groups within the                   existing company groups formed according to their financial performance; the                   grouping was based on the similarity of values of the identified factors of corporate                   performance. Consequently, these groups, which were created using the quantitative                   approach, had to be interpreted using a qualitative approach. It was necessary to                   synthesize the values of the individual factors and other explanatory variables, taking                   into account the variability of these values, so that a representative of each of these                   groups of companies could be characterized in the terminology of business studies.                   Such a process is obviously challenging in terms of the substantive knowledge of the                   issues, inventiveness and imagination. Nevertheless, it was this step that finished the                   implementation of the entire task, and it was possible to economically assess the                   correctness and relevance of the results achieved.                    In conclusion, we can say that even with the great complexity of the task whose                   solution was very laborious, the results obtained can be regarded as beneficial. The                   objective laid down in the project can be considered satisfied, as a series of                   experiments verified the effective applicability of feature selection methods from the                   field of statistical pattern recognition in identifying the factors of financial                   performance of companies.","Castek_1_Castek  23.1.2015  7:38  Stránka 159                                                                                                   159                                  8 Bibliography                           [1]  ABOR, J., BIEPKE, N. (2007). Corporate Governance, Ownersip Structure and                        Performance of SMEs in Ghana: Implications for Financing Opportunities. Corporate                        Governance, Vol. 3, Issue 7, pp. 288–300. DOI: 10.1108/14720700710756562                   [2]  ALEXE, G., ALEXE, S., HAMMER, P. L., VIZVARI, B. (2006). 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DOI:                        10.1016/j.patrec.2008.11.012","Castek_1_Castek  23.1.2015  7:38  Stránka 167                                                                                                   167                     List of Figures                     Figure 1-1: The methodology of previous research activities             13                   Figure 1-2: Methodology of current research activities                  17                   Figure 2-3: Quintiles method                                            31                   Figure 2-4: Descriptive statistics of informativeness values produced by different                        methods                                                            34                   Figure 2-5: Summary of the SFFS algorithm output for the exponent method   34                   Figure 2-6: Fluctuation analysis                                        35                   Figure 3-7: Peaking Phenomenon – correct classification rate is a nonmonotonous                        function of the number of features                                 43                   Figure 3-8a: Scheme of FS                                               43                   Figure 3-8b: Scheme of FE                                               43                   Figure 3-9: Feature selection algorithms can be viewed as black box procedures                        generating a sequence of candidate subsets with respective criterion values,                        among which intermediate solutions are chosen                      47                   Figure 3-10: In this 2D case nor feature 1 nor 2 is sufficient to distinguish patterns from                        classes of rectangles and circles. Only when information from both features is                        combined, classes can be separated (dotted line)                   48                   Figure 3-11: Sequential Forward Floating Selection Algorithm            50                   Figure 3-12: Comparing the course of search (current subset size depending on time)                        in standard sequential search methods                              51                   Figure 3-13: Sub-optimal FS methods’ optimization performance on 3-NN wrapper  60                   Figure 3-14: Sub-optimal FS methods’ performance verified using 3-NN on                        independent data                                                   60                   Figure 4-15a: Informativeness of isolated features                      66                   Figure 4-15b: Synergic effect of more features                          66                   Figure 4-16: Cases of possible univariate analysis failure (illustrative example). Let the                        dots represent the companies of poor CFP and the rectangles represent the well                        performing companies. Univariate analysis is not capable of revealing a)                        competitiveness factor redundancy, b) multi-variate factor dependency leading                        to crucial model accuracy improvement in higher than one-dimensional                        subspace.                                                          69                   Figure 4-17: Comparing SFFS and DAF stability and performance when selecting 5 or                        15 features out of 37, with k-NN for k=1, 2, 3. Diamonds show k-NN accuracy                        achieved; other lines show stability                               70                   Figure 4-18: Given existing samples S , .., S and distance function d(), the yn value of                                                     3                                                 1                        sample Sn is predicted as sum over w * y for i=1, .., 3, where wi reflects d(S ,                                                         i                                                                                     n                                                      i                        S ) distance from 1-D Gaussian kernel centered in S i              75                         i                   Figure 4-19: Errors of four regression models – each dot represents a company,                        positioned according to its Assets Growth (GA) and Return on Assets (ROA)                        values, a higher dot diameter depicts a higher regression error; black and grey                        colours depict its positive or negative value, respectively: a) 1-Nearest Neighbour                        with missing values substituted by mean values, b) Kernel Regressor with missing                        values substituted by mean values, c) 1-Nearest Neighbour with missing values","Castek_1_Castek  23.1.2015  7:38  Stránka 168                  168                          treated pessimistically, d) (best) Kernel Regressor with missing values treated                        pessimistically.                                                   76                   Figure 4-20: Importance of single company characteristics according to the best-                        achieved regression model. The graph represents growing subsets of features,                        features added according to the highest DAF1 coefficients. Note that model                        accuracy markedly improves after adding the first 8 features, and then after                        adding roughly the next 7 features.                                77                   Figure 4-21: Importance of single company characteristics according to best-achieved                        classification using 1-NN classifier and 3-class data. The graph represents                        growing subsets of features, features added according to highest DAF1                        coefficients. Note that model accuracy markedly improves after adding the first                        8 features, and then after adding roughly the next 10 features.    79                   Figure 4-22: Comparing Euclidean distance to alternative distances. Higher-order                        distance functions improve the accuracy of the kernel-based regression model                        on subspaces roughly of up to D/2 where D is the total number of features  81                   Figure 4-23: Comparing accuracy of a pseudo-kernel regression model with a globally                        optimized multiplication constant m to a model with a locally optimized m.                        Note that a local optimization of m (optimization on subspace instead on full                        space) improves accuracy when a small number of features is used   81                   Figure 4-24: Comparing the accuracy of default model to that of the improved model.                        Comparison provided separately for 37- and 74-dimensional dataset representing                        the same domain. Default configuration compared to the best configuration                        identified in this paper                                           85                   Figure 5-25: The effect of industry on financial performance controlled for the company                        size                                                               96                   Figure 5-26: The effect of company size on financial performance controlled for the                        industry                                                           97                   Figure 5-27: The combined effect of company size and industry on financial                        performance                                                        97                     List of Tables                    Table 3-1: Evolution of sequential search methods                       49                   Table 3-2: Single features in descending order, first best 7 then last worst 7, according                        to individual criterion values (i.e., “individual discriminative power”), 4-class,                        38-dimensional Australian credit scoring data                      53                   Table 4-3: Analogy of problems of statistical pattern recognition and the problem of                        determining competitiveness factors                                68                   Table 4-4: Comparing feature orderings yielded by model using Euclidean distance and                        L7 distance                                                        82                   Table 4-5: Comparing feature orderings yielded by a model using a globally versus                        locally optimized kernel width multiplier constant. Euclidean distance is used in                        both cases.                                                        84                   Table 4-6: Top 25 features selected using the optimized model on 74-dim and 37-dim                        data                                                               86","Castek_1_Castek  23.1.2015  7:38  Stránka 169                                                                                                   169                     Table 5-7: Frequency distribution of a categorized company size         93                   Table 5-8: The association between the company size and the financial performance  93                   Table 5-9: The association between the industry and the financial performance  94                   Table 5-10: The association between the industry and the financial performance,                        controlling for the size of the company: statistics                95                   Table 5-11: The association between the industry and the financial performance,                        controlling for the size of the company: differences in CFP        95                   Table 5-12: The influence of company size on financial performance, controlling for                        the industry: statistics                                           96                   Table 5-13: Variables describing the internal environment of a company: bivariate                        correlations with CFP                                              98                   Table 5-14: Summary of the internal factors regression model            99                   Table 5-15: Coefficients of the internal factors regression model      100                   Table 5-16: Variables describing the external environment of a company: bivariate                        correlations with CFP                                             101                   Table 5-17: Summary of the external factors regression model           102                   Table 5-18: Coefficients of the external factors regression model      103                   Table 5-19: Contents of the variables describing the stakeholder orientation and                        characteristics of an organizational structure                    104                   Table 5-20: Variables describing stakeholder orientation of an enterprise and                        characteristics of an organizational structure: bivariate correlations with CFP  105                   Table 5-21: Summary of the regression model describing stakeholder orientation of an                        enterprise and characteristics of its organizational structure    106                   Table 5-22: Coefficients of the regression model describing stakeholder orientation of                        an enterprise and characteristics of its organizational structure  107                   Table 5-23: Contents of variables describing the ownership and property structure  108                   Table 5-24: Variables describing the ownership and property structure: bivariate                        relationships with CFP                                            109                   Table 5-25: Summary of the regression model describing the ownership and property                        structure                                                         110                   Table 5-26: Coefficients of the regression model describing the ownership and property                        structure                                                         111                   Table 5-27: Contents of variables describing the stakeholder group of employees  112                   Table 5-28: Variables describing the stakeholder group of employees: bivariate                        relationships with CFP                                            113                   Table 5-29: Summary of the regression model describing the stakeholder group of                        employees                                                         115                   Table 5-30: Coefficients of the regression model describing the stakeholder group of                        employees                                                         115                   Table 5-31: Contents of variables describing customers of a company    117                   Table 5-32: Variables describing customers: bivariate relationships with CFP  117                   Table 5-33: Summary of the regression model describing the stakeholder group of                        customers                                                         119                   Table 5-34: Coefficients of the regression model describing the stakeholder group of                        customers                                                         119","Castek_1_Castek  23.1.2015  7:38  Stránka 170                  170                     Table 5-35: Contents of variables describing suppliers of a company    120                   Table 5-36: Variables describing suppliers of a company: bivariate relationships with                        CFP                                                               121                   Table 5-37: Summary of the regression model describing the stakeholder group of                        suppliers                                                         122                   Table 5-38: Coefficients of the regression model describing the stakeholder group of                        suppliers                                                         123                   Table 5-39: Variables describing CSR activities of a company: bivariate relationships                        with CFP                                                          124                   Table 5-40: Summary of the regression model describing corporate social performance  125                   Table 5-41: Coefficients of the regression model describing corporate social                        performance                                                       125                   Table 5-42: Summary of the comprehensive regression model              127                   Table 5-43: Coefficients of the comprehensive regression model         128                   Table 6-44: Overview of variables                                      130                   Table 6-45: Summary of frequencies of categorical variables in the sample, group A and                        its subgroups                                                     153                   Table 6-46: Summary of average values of chosen variables in the sample, group A and                        its subgroups                                                     155                      List of Graphs                     Graph 2-1: Clusters of cluster analysis                                 27                   Graph 2-2: Hyperbola                                                    29                   Graph 6-3: Relative frequency of quartiles in manufacturing and construction   131                   Graph 6-4: Relative frequencies of quartiles in private limited companies and in joint                        stock companies                                                   132                   Graph 6-5: Relative frequencies of quartiles according to company size  133                   Graph 6-6: Relative frequencies of quartiles according to concern membership  133                   Graph 6-7: Relative frequencies of quartiles in companies with and without FDI  134                   Graph 6-8: Relative frequencies of quartiles according to the ownership concentration  135                   Graph 6-9: Relative frequencies of quartiles according to generic strategy  136                   Graph 6-10: Share of companies with predominant exports in the quartiles  137                   Graph 6-11: The average span of control in the quartiles               137                   Graph 6-12: The average upper limit of the motivation components of workers’ wages                        in the quartiles                                                  138                   Graph 6-13: The average upper limit of the motivation components of top-managers’                        salaries in the quartiles                                         139                   Graph 6-14: The average percentage of technical and administrative staff in the quartiles  139                   Graph 6-15: The average percentage of workers in the quartiles         140                   Graph 6-16: The average percentage of women in the quartiles           141                   Graph 6-17: The average frequency of reasons for the staff turnover rate (from the                        employee’s initiative) in the quartiles                           141                   Graph 6-18: The average tangible assets level in the quartiles         142","","Castek_1_Castek  23.1.2015  7:38  Stránka 172                           Board of Scientific Editors:                     prof. PhDr. Ladislav Rabušic, CSc.                   Mgr. Iva Zlatušková                   Ing. Radmila Droběnová, Ph.D.                   Mgr. Michaela Hanousková                   doc. PhDr. Jana Chamonikolasová, Ph.D.                   doc. JUDr. Josef Kotásek, Ph.D.                   Mgr. et Mgr. Oldřich Krpec, Ph.D.                   prof. PhDr. Petr Macek, CSc.                   PhDr. Alena Mizerová                   doc. Ing. Petr Pirožek, Ph.D.                   Mgr. Petra Polčáková                   doc. RNDr. Lubomír Popelínský, Ph.D.                   Mgr. Kateřina Sedláčková, Ph.D.                   prof. RNDr. David Trunec, CSc.                   prof. MUDr. Anna Vašků, CSc.                   prof. PhDr. Marie Vítková, CSc.                   doc. Mgr. Martin Zvonař, Ph.D.                             Pavel Pudil, Ladislav Blažek, Ondřej Částek, Petr Somol, Jana Pokorná, Maria Králová                    Identifying Corporate Performance Factors Based                   on Feature Selection in Statistical Pattern Recognition.                   METHODS, APPLICATION, INTERPRETATION                     Editorial Board: doc. Ing. Petr Pirožek, Ph.D., doc. Ing. Petr Suchánek, Ph.D.,                   doc. RNDr. Milan Viturka, CSc., doc. Ing. Vladimír Hyánek, Ph.D., Ing. Eva Hýblová, Ph.D.,                   Ing. Daniel Němec, Ph.D., Ing. Mgr. Markéta Matulová, Ph.D.                   Cover design: RNDr. Petr Somol, Ph.D.                   Layout and typeset: Lea Novotná                   Published by Masaryk University in cooperation with University of Economics, Prague                   Brno 2014                   First Edition                     ISBN 978-80-210-7557-3                   ISBN 978-80-210-7672-3 (online : pdf)                   DOI: 10.5817/CZ.MUNI.M210-7557-2014","9 788021 075573                                                   2 0 14                                                                                   ISBN 978-80-210-7557-3                                                                                   DOI: 10.5817/CZ.MUNI.M210-7557-2014                                      Administration, Masaryk University                                                                                                  PUDIL,  BLAŽEK   et al.                                           Faculty of Economics and                                                      \&                                       University of Economics, Prague                                            Faculty of Management                                                                                                  2014                                                                                                  Identifying Corporate Performance Factors Based on Feature Selection                                                                                                                                                                                                               Faculty of Management                                                                                                                                                                                                    University of Economics, Prague                                                                                                  Identifying Corporate Performance Factors Based on Feature Selection                                                                                                                                                                                                                                             \&                                                                                                                                                                                                             Faculty of Economics and                                                                                                                                          Faculty of Management                                                                                                                                                                                               Administration, Masaryk University                                                                                                                                     University of Economics, Prague                                                                                                                                                   \&                                                                                                                                         Faculty of Economics and                                                                                                                                    Administration, Masaryk University  Identifying Corporate Performance                                                                                                                                                               Factors Based on Feature Selection in                                                                                                                                                                              Statistical Pattern Recognition                                                                                                                           Identifying Corporate Performance                   M E T H O D S ,   A P P L I C AT I O N ,   I N T E R P R E TAT I O N                                                                                                                          Factors Based on Feature Selection in                                      Pavel Pudil, Ladislav Blažek,                                                                                                                              Statistical Pattern Recognition                    Ondřej Částek, Petr Somol, Jana Pokorná,                                                                                                                                                                                                                          Maria Králová                                                                                                                              METHODS, APPLICATION, INTERPRETATION                                                                                                                                      Pavel Pudil, Ladislav Blažek,                                                                                                                               Ondřej Částek, Petr Somol, Jana Pokorná,                                                                                                                                            Maria Králová                                                                           2014                                                                                                                                                     2014                                                                                                          2014                                        Faculty of Management anagement                              Faculty of M                          Universit University of Economics, Praguey of Economics, Prague                                        \&        \&                             Faculty of E                                      Faculty of Economics and conomics and                                                                                                  PUDIL,  BLAŽEK   et al.                        Administr                                 Administration, Masaryk Universityation, Masaryk University                                                                  DOI: 10.5817/CZ.MUNI.M210-7557-2014                                        2 0 14  2 0 14                                                                                   88021            PUDIL,  BLAŽEK   et al.  2014  Identifying Corporate Performance Factors Based on Feature Selection  Factors Based on Feature Selection in                                            2 0 14                                                   2 0 14                                                                                    DOI: 10.5817/CZ.MUNI.M210-7557-2014                                                                     DOI: 10.5817/CZ.MUNI.M210-7557-2014                                                                                                                                                                           2014                                                                                                                                                 Maria Králová                                                                                                                               Ondřej Částek, Petr Somol, Jana Pokorná,                                                                                                                                     Pavel Pudil, Ladislav Blažek,                                                                                                                               METHODS, APPLICATION, INTERPRETATION                                                                                                                                Statistical Pattern Recognition                                                                                                                              Identifying Corporate Performance                                                                                                                                        Administration, Masaryk University                                                                                                                                         Faculty of Economics and                                                                                                                                                   \&                                                                                                                                     University of Economics, Prague                                                                                                                                          Faculty of Management"];