Statistical Modeling for Management

Books

Graeme D. Hutcheson & Luiz Moutinho

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  • Chapters
  • Front Matter
  • Back Matter
  • Subject Index
  • Dedication

    To a number of very patient people (You know who you are), Andrea, Alex, …and all Portuguese waiters.

    Graeme Hutcheson
    Luiz Moutinho

    Copyright

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    List of Tables

    • 1 Measurement Scales 1
      • 1.1 Examples of Interval and Ratio Scales 4
      • 1.2 An Example of Categorized Continuous Data 5
      • 1.3 Ordered Categorical Coding of Army Rank: Example I 7
      • 1.4 Ordered Categorical Coding of Army Rank: Example II 8
      • 1.5 Unordered Categorical Coding of Army Rank 8
      • 1.6 Continuous Variables Coded As Ordered Categories 9
      • 1.7 A Continuous Variable Coded As Ordered Categorical Data 10
      • 1.8 Representing Age Using Ordered Categories 10
      • 1.9 Mis-Coding an Ordered Categorical Variable 11
      • 1.10 Highest Educational Attainment 12
      • 1.11 Unordered Categorical Data: Coding Example I 13
      • 1.12 Unordered Categorical Data: Coding Example II 14
      • 1.13 Number of Cars Sold in a Year 14
    • 2 Modeling Continuous Data 17
      • Simple OLS Regression 19
      • 2.1 Data: Ice Cream Consumption 20
      • 2.2 Regression Parameters 22
      • 2.3 Predictions of Consumption 23
      • 2.4 Computing the Deviance for the Model “Consumption = α” 25
      • 2.5 Computing the Deviance for the Model “Consumption = α + β Temperature” 26
      • 2.6 Assessing Significance By Comparing Model Deviances 27
      • 2.7 Analysis of Deviance Table: The Significance of Variables 28
      • 2.8 Estimating the Significance of Individual Parameters Using T-Statistics 28
      • 2.9 Regression Parameters 30
      • 2.10 Confidence Intervals 30
      • 2.11 Predictions of Consumption 32
      • 2.12 Assessing Significance By Comparing Model Deviances: Individual Variables 32
      • 2.13 Assessing Significance By Comparing Model Deviances: Groups of Variables 33
      • 2.14 Analysis of Deviance Table: The Significance of Variables 34
      • 2.15 Estimating the Significance of Individual Parameters Using T-Statistics 35
      • 2.16 Data: The Price of Whiskey (Comparing 2 Groups) 37
      • 2.17 Price of whiskey: “Ownership” Dummy Coded 39
      • 2.18 Regression Parameters 39
      • 2.19 Confidence Intervals 39
      • 2.20 Assessing Significance By Comparing Model Deviances 41
      • 2.21 Analysis of Deviance Table: The Significance of Variables 41
      • 2.22 Estimating the Significance of Individual Parameters Using T-Statistics 42
      • 2.23 Data: The Price of Whiskey (Comparing Three Groups) 42
      • 2.24 The Indicator Method of Dummy Coding “Ownership” 43
      • 2.25 Regression Parameters 43
      • 2.26 Confidence Intervals 44
      • 2.27 Assessing Significance By Comparing Model Deviances 45
      • 2.28 Analysis of Deviance Table: The Significance of Variables 46
      • 2.29 Estimating the Significance of Individual Parameters Using T-Statistics 46
      • 2.30 The Two Group Whiskey Data: T-Test 47
      • 2.31 The Three Group Whiskey Data: ANOVA 47
      • 2.32 Data: Quality Ratings of Stores 48
      • 2.33 Regression Parameters 49
      • 2.34 Confidence Intervals 50
      • 2.35 Predicting the Quality of the Stores 51
      • 2.36 Assessing the Significance of “Store” By Comparing Model Deviances 52
      • 2.37 Assessing the Significance of “Subject” By Comparing Model Deviances 52
      • 2.38 Analysis of Deviance Table: The Significance of Variables 52
      • 2.39 Estimating the Significance of Individual Parameters Using T-Statistics 53
      • 2.40 Regression Parameters 54
      • 2.41 Analysis of Deviance Table: The Significance of variables 54
      • 2.42 The Two Group Store Data: Related T-Test 55
      • 2.43 The Three Group Store Data: Related ANOVA 55
    • 3 Modeling Dichotomous Data 57
      • 3.1 The Logit Transformation 61
      • 3.2 Data: Example for Illustrating Logistic Regression 63
      • 3.3 Regression Parameters 63
      • 3.4 Confidence Intervals 65
      • 3.5 Predicted Probabilities 66
      • 3.6 Assessing Significance By Comparing Model Deviances 68
      • 3.7 Analysis of Deviance Table: The Significance of Variables 68
      • 3.8 Estimating the Significance of Individual Parameters Using the Z-Statistic 69
      • 3.9 Regression Parameters 72
      • 3.10 Confidence Intervals 72
      • 3.11 Predicted Probabilities of Union Membership at a Selection of Wages and Ages 74
      • 3.12 Assessing Significance By Comparing Model Deviances 74
      • 3.13 Analysis of deviance table: the significance of variables 75
      • 3.14 Estimating the Significance of Individual Parameters Using the Z-Statistic 75
      • 3.15 Deviation Dummy Variable Coding of ‘Occupation’ 76
      • 3.16 Regression Parameters 78
      • 3.17 Predicted Probabilities of Union Membership 79
      • 3.18 Assessing Significance By Comparing Model Deviances 80
      • 3.19 Analysis of Deviance Table: The Significance of Variables 81
      • 3.20 Estimating the Significance of Individual Parameters Using the Z-Statistic 81
    • 4 Modeling Ordered Data 83
      • Simple Proportional Odds 85
      • 4.1 Data: Ice Cream Consumption Represented as Ordered categories 86
      • 4.2 Test of the Proportional Odds Assumption 88
      • 4.3 Regression Parameters 88
      • 4.4 Confidence Intervals 89
      • 4.5 Predicted Consumption 90
      • 4.6 Assessing Significance By Comparing Model Deviances 92
      • 4.7 Analysis of Deviance Table: The Significance of Variables 92
      • 4.8 Estimating the Significance of Individual Parameters Using T-Statistics 93
      • 4.9 Test of the Proportional Odds Assumption 94
      • 4.10 Regression Parameters 96
      • 4.11 Confidence Intervals 96
      • 4.12 Predicted Probabilities 97
      • 4.13 Assessing Significance By Comparing Model Deviances 98
      • 4.14 Analysis of Deviance Table: The Significance of Variables 99
      • 4.15 Estimating the Significance of Individual Parameters Using T-Statistics 99
      • 4.16 Comparing Proportional Odds and OLS Regression Models 100
      • 4.17 Test of the Proportional Odds Assumption 102
      • 4.18 Regression Parameters 103
      • 4.19 Confidence Intervals 103
      • 4.20 Predicted Probabilities 104
      • 4.21 Assessing Significance By Comparing Model Deviances 105
      • 4.22 Analysis of Deviance Table: The Significance of Variables 105
      • 4.23 Estimating the Significance of Individual Parameters Using T-Values 106
      • 4.24 Data: Ranked Price of Whiskey 108
      • 4.25 Test of the Proportional Odds Assumption 108
      • 4.26 Regression Parameters 109
      • 4.27 Confidence Intervals 110
      • 4.28 Predicted Probabilities 110
      • 4.29 Assessing Significance By Comparing Model Deviances 111
      • 4.30 Estimating the Significance of Individual Parameters Using T-Values (Reference Category for Variable ‘Funded’ = State-Private Partnership). 111
      • 4.31 Estimating the Significance of Individual Parameters Using T-Values (Reference Category for Variable ‘Funded’= Private) 112
      • 4.32 Data: Ranked Quality Ratings of Stores 114
      • 4.33 Test of the Proportional Odds Assumption 115
      • 4.34 Regression Parameters 116
      • 4.35 Confidence Intervals 117
      • 4.36 Predicted Probabilities 118
      • 4.37 Assessing Significance By Comparing Model Deviances 118
      • 4.38 Analysis of Deviance Table: Significance of Variables 118
      • 4.39 Estimating the Significance of Individual Parameters Using T-Values 119
    • 5 Modeling Unordered Data 121
      • 5.1 Data: Supermarket Choice 124
      • 5.2 Regression Parameters 125
      • 5.3 Confidence Intervals 126
      • 5.4 Predicted Probabilities 127
      • 5.5 Assessing Significance By Comparing Model Deviances 128
      • 5.6 Analysis of Deviance Table: Significance of Variables 128
      • 5.7 Estimating the Significance of Individual Parameters Using Wald and Z-Statistics (Reference Supermarket = Sainsburys) 129
      • 5.8 Estimating the Significance of Individual Parameters Using Wald and Z-Statistics (Reference Supermarket = Solo) 130
      • 5.9 Regression Parameters 132
      • 5.10 Confidence Intervals 134
      • 5.11 Predicted Probabilities 134
      • 5.12 Assessing Significance By Comparing Model Deviances 135
      • 5.13 Analysis of Deviance Table: Significance of Variables 136
      • 5.14 Estimating the Significance of Individual Parameters Using Wald and Z-Statistics 136
      • 5.15 Data: Unordered Categorical Data From an Unrelated Groups Design 139
      • 5.16 Contingency Table 139
      • 5.17 Regression Parameters 141
      • 5.18 Confidence Intervals 142
      • 5.19 Predicted Probabilities 142
      • 5.20 Assessing Significance By Comparing Model Deviances 143
      • 5.21 Analysis of Deviance Table: Significance of Variables 143
      • 5.22 Estimating the Significance of Individual Parameters Using Wald and Z-Statistics (Outcome Reference Category = Accept) 144
      • 5.23 Estimating the Significance of Individual Parameters Using Wald and Z-Statistics (Outcome Reference Category = Undecided) 144
      • 5.24 Data: Unordered Categorical Data From a Related Groups Design 146
      • 5.25 Regression Parameters 147
      • 5.26 Confidence Intervals 148
      • 5.27 Predicted Probabilities 149
      • 5.28 Assessing Significance By Comparing Model Deviances 149
      • 5.29 Analysis of Deviance Table: Significance of Variables 150
      • 5.30 Estimating the Significance of Individual Parameters Using Wald and Z-Statistics 151
    • 6 Neural Networks 153
      • 6.1 Network Weights for Male Buyers 170
      • 6.2 Network Weights for Female Buyers 171
      • 6.3 Labels Given to the Hidden Nodes 172
    • 7 Approximate Algorithms for Management Problems 177
    • 8 Other Statistical, Mathematical and Co-Pattern Modeling Techniques 191
      • 8.1 5 Set of Propositional Rules (C5 Ra) 195
      • 8.2 5 Set of Propositional Rules (C5 Rb) 196
      • 8.3 Classification Precision 197
      • 8.4 Fuzzy Set Theory 204
      • 8.5 Example of a Decision Table 211

    List of Figures

    • 1 Measurement Scales 1
      • 1.1 The Relationship the Attribute, the Data and the Analysis 2
    • 2 Modeling Continuous Data 17
      • 2.1 A Scatterplot Showing the Relationship Between Ice Cream Consumption and Outdoor Temperature and the Associated ols Regression Model 21
      • 2.2 Residuals for the Model “Consumption = α” 24
      • 2.3 Residuals for the Model “Consumption = α + β Temperature” 25
      • 2.4 A Pictorial Representation of an Unrelated Groups Design 38
      • 2.5 A Pictorial Representation of a Dependent Groups Design 48
    • 3 Modeling Dichotomous Data 57
      • 3.1 Success and the Experience of the Sales Staff 58
      • 3.2 The Probability of Success and the Experience of the Sales Staff 59
      • 3.3 The Log Odds of Success and the Experience of the Sales Staff 60
      • 3.4 A Logit Model of the Probability of Success and the Experience of the Sales Staff 62
      • 3.5 Union Membership and Wage 64
      • 3.6 Logistic Regression Model of Union Membership and Wage 67
      • 3.7 Probability of Being a Union Member and Age 70
      • 3.8 Relationship Between Wage and Age 71
      • 3.9 Probability of Being a Union Member for Different Genders and Occupations 77
    • 4 Modeling Ordered Data 83
      • 4.1 Temperature and Consumption Level of Ice Cream 87
      • 4.2 Predicted Probabilities for Each Group Given Temperature 91
      • 4.3 Boxplots Showing Relationships Between Each Explanatory Variable and the Level of Consumption 94
      • 4.4 Matrix Scatterplot Showing Relationships Between the Explanatory Variables 95
      • 4.5 Level of Consumption and Type of Advertising Used 101
      • 4.6 A Pictorial Representation of an Unrelated Groups Design 108
      • 4.7 Average Ranked Price of Whiskey for Each Type of Ownership 113
      • 4.8 A Pictorial Representation of a Dependent Groups Design 114
      • 4.9 Average Rated Quality for Each Store 117
    • 5 Modeling Unordered Data 121
      • 5.1 Selected Supermarket and Average Salary 125
      • 5.2 Selected Supermarket, Average Salary and Car Use 131
      • 5.3 Relationship Between Average Salary and Car Use 132
      • 5.4 A Pictorial Representation of an Unrelated Groups Design 138
      • 5.5 An Association Plot 140
      • 5.6 A Pictorial Representation of a Dependent Groups Design 145
    • 6 Neural Networks 153
      • 6.1 A Neural Network with One Hidden Layer 156
      • 6.2 The Sigmoid Function 160
      • 6.3 Connections Operate Between All Inputs and All Kohonen Nodes 165
      • 6.4 Neural Network Used in Car Buyer Analysis 169
    • 7 Approximate Algorithms for Management Problems 177
      • 7.1 Example of a Move Applied to a Tree With Five Terminal Nodes 183
    • 8 Other Statistical, Mathematical and Co-Pattern Modeling Techniques 191
      • 8.1 Procedural Steps for Correspondence Analysis 201
      • 8.2 Success and the Experience of the Sales Staff 202
      • 8.3 Output of Logistic Equation for Varying r 216

    Preface

    This book is aimed at doctoral students and researchers working in Management and other social science subjects. It aims to provide a resource for training in basic data analysis and also provide some information about a number of more specialized techniques used in the management field. The contents have been compiled and written over a number of years during which time Graeme Hutches on and Luiz Moutinho have been involved in teaching postgraduate students, academic staff and researchers research methods, data analysis and statistical modeling. The material presented here provides some basic notes for these courses and we are indebted to the many students who have attended our training sessions and commented on the notes and examples. Although some complex issues are addressed in later chapters, the main body of the book attempts to explain how generalized linear models can be applied to a great range of common research questions and research designs for different types of data. In particular, this material is designed to be accessible to all postgraduate students. Although an extensive statistical or mathematical knowledge is not assumed, readers might benefit from attending an introductory course on statistics, or by consulting one of the many basic statistical text books that are available.

    This book can be broadly divided into two parts, one that deals with generalized linear models (GLMs) and one that deals with a number of other techniques that may be applied in management research. As the objective of the former is for teaching, these chapters are accompanied by data sets that can be analysed and the results compared to the output provided. The outputs are given in a software-neutral manner so that these can be compared to the outputs from a number of different statistical packages (in Management, SPSS is often used, although we strongly recommend the use of R, a package that is described in more detail below).

    The first five chapters of the book describe how data can be classified, coded and analyzed using a number of generalized linear modeling techniques. The aim has been to provide a theoretically-consistent method for modeling continuous, ordered and unordered categorical data. The analysis of experimental data is discussed within the main chapters in a way that makes clear the links between the hypothesis tests and the regression models. Chapters 6, 7 and 8 deal with other techniques (such as neural networks and approximate algorithms) that may also be of interest to researchers in the management field.

    The data that are used in this book are available for download at http://www.sagepub.co.uk/hutcheson_moutinho and are saved as tab-delimited text to enable them to be simply imported into a number of statistical packages and spreadsheets. The data used and where they are presented in the book are shown in the Table below.

    The statistics for this book were mainly analyzed using R (see the R Development Core Team, 2007 and the R website at http://www.r-project.org/) and a number of associated packages (the most notable being the graphical user interface ‘R Commander”, written by John Fox, 2005). The use of R Commander, in particular, has enabled us to teach statistics to groups with little or no previous statistical experience whilst utilizing the power of the R programme. This combination of packages has proved to be so successful that and we have now adopted R as the only statistics package we use for our courses. Its ease of use along with its free download, multi-platform capabilities and extraordinary range of techniques, manuals (in many languages), examples and a generous community make it a wonderful resource for all data analysts.

    Even though R may not be the easiest package to master, there are many resources available to help with analysis and graphics. Some of the resources I have found to be particularly useful have been Venables, Smith and the R Development Core Team (2002), Dalgaard (2002), Crawley (2005), Verzani (2005), Faraway (2005), Fox (2002), Venables and Ripley (2002), Murrell (2006) and Maindonald and Braun (2003).

    This book was typeset by Graeme Hutcheson at Manchester University using and a debt of gratitude is owed to Donald Knuth, the creator of (Knuth, 1984), Leslie Lamport who built this into the documentation system, and to the many contributors who freely give their time and expertise to support this package (see, for example, Grätzer (2000), Kopka and Daly (2003), Lipkin (1999) and Mittelbach et al., (2004)). Full details of the project are available on the web at ‘http://www.latexproject.org/’.

    Graeme Hutcheson, Manchester University
    Luiz Moutinho, Glasgow University
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