Statistical Analysis of Management Data (eBook)

Contents 7
Preface 12
1. Introduction 13
1.1 Overview 13
1.2 Objectives 14
1.2.1 Develop the Student’s Knowledge of the Technical Details of Various Techniques for Analyzing Data 14
1.2.2 Expose the Students to Applications and “Hand-on” Use of Various Computer Programs for Carrying Out Statistical Analyses of Data 14
1.3 Types of Scales 15
1.3.1 Definition of Different Types of Scales 16
1.3.2 The Impact of the Type of Scale on Statistical Analysis 16
1.4 Topics Covered 17
1.5 Pedagogy 18
References 20
2. Multivariate Normal Distribution 21
2.1 Univariate Normal Distribution 21
2.2 Bivariate Normal Distribution 21
2.3 Generalization to Multivariate Case 23
2.4 Tests About Means 24
2.4.1 Sampling Distribution of Sample Centroids 24
2.4.2 Significance Test: One-sample Problem 25
2.4.3 Significance Test: Two-sample Problem 27
2.4.4 Significance Test: K-sample Problem 29
2.5 Examples 31
2.5.1 Test of the Difference Between Two Mean Vectors – One- Sample Problem 31
2.5.2 Test of the Difference Between Several Mean Vectors – K-sample Problem 33
2.6 Assignment 37
References 39
Basic Technical Readings 39
Application Readings 39
3. Measurement Theory: Reliability and Factor Analysis 41
3.1 Notions of Measurement Theory 41
3.1.1 Definition of a Measure 41
3.1.2 Parallel Measurements 41
3.1.3 Reliability 41
3.1.4 Composite Scales 42
3.2 Factor Analysis 45
3.2.1 Axis Rotation 45
3.2.2 Variance Maximizing Rotations (Eigenvalues/vectors) 46
3.2.3 Principal Component Analysis 49
3.2.4 Factor Analysis 50
3.3 Conclusion - Procedure for Scale Construction 55
3.3.1 Exploratory Factor Analysis 55
3.3.2 Confirmatory Factor Analysis 56
3.3.3 Reliability-Coefficient 56
3.4 Application Examples 56
3.5 Assignment 65
References 66
Basic Technical Readings 66
Application Readings 66
4. Multiple Regression with a Single Dependent Variable 67
4.1 Statistical Inference: Least Squares and Maximum Likelihood 67
4.1.1 The Linear Statistical Model 67
4.1.2 Point Estimation 69
4.1.3 Maximum Likelihood Estimation 71
4.1.4 Properties of Estimator 73
4.2 Pooling Issues 77
4.2.1 Linear Restrictions 77
4.2.2 Pooling Tests and Dummy Variable Models 79
4.2.3 Strategy for Pooling Tests 81
4.3 Examples of Linear Model Estimation with SAS 83
4.4 Assignment 87
References 88
Basic Technical Readings 88
Application Readings 89
5. System of Equations 91
5.1 Seemingly Unrelated Regression (SUR) 91
5.1.1 Set of Equations with Contemporaneously Correlated Disturbances 91
5.1.2 Estimation 93
5.1.3 Special Cases 94
5.2 A System of Simultaneous Equations 95
5.2.1 The Problem 95
5.2.2 Two Stage Least Squares: 2SLS 99
5.2.3 Three Stage Least Squares: 3SLS 99
5.3 Simultaneity and Identification 100
5.3.1 The Problem 100
5.3.2 Order and Rank Conditions 101
5.4 Summary 103
5.4.1 Structure of Matrix 103
5.4.2 Structure of Matrix 104
5.4.3 Test of Covariance Matrix 104
5.4.4 3SLS versus 2SLS 105
5.5 Examples Using SAS 105
5.5.1 Seemingly Unrelated Regression Example 105
5.5.2 Two Stage Least Squares Example 111
5.5.3 Three Stage Least Squares Example 113
5.6 Assignment 115
References 116
Basic Technical Readings 116
Application Readings 116
6. Categorical Dependent Variables 117
6.1 Discriminant Analysis 117
6.1.1 The Discriminant Criterion 117
6.1.2 Discriminant Function 120
6.1.3 Classification and Fit 121
6.2 Quantal Choice Models 124
6.2.1 The Difficulties of the Standard Regression Model with Categorical Dependent Variables 124
6.2.2 Transformational Logit 125
6.2.3 Conditional Logit Model 129
6.2.4 Fit Measures 132
6.3 Examples 133
6.3.1 Example of Discriminant Analysis Using SAS 133
6.3.2 Example of Multinomial Logit – Case 1 Analysis Using LIMDEP 140
6.3.3 Example of Multinomial Logit – Case 2 Analysis Using LOGIT. EXE 142
6.3.4 Example of Multinomial Logit – Case 2 Analysis Using LIMDEP 145
6.4 Assignment 147
References 148
Basic Technical Readings 148
Application Readings 148
7. Rank Ordered Data 149
7.1 Conjoint Analysis – MONANOVA 149
7.1.1 Effect Coding Versus Dummy Variable Coding 149
7.1.2 Design Programs 154
7.1.3 Estimation of Part-worth Coefficients 155
7.2 Ordered Probit 156
7.3 Examples 159
7.3.1 Example of MONANOVA Using PC-MDS 159
7.3.2 Example of Conjoint Analysis Using SAS 163
7.3.3 Example of Ordered Probit Analysis Using LIMDEP 163
7.4 Assignment 166
References 168
Basic Technical Readings 168
Application Readings 168
8. Error in Variables – Analysis of Covariance Structure 171
8.1 The Impact of Imperfect Measures 171
8.1.1 Effect of Errors-in-variables 171
8.1.2 Reversed Regression 173
8.1.3 Case with Multiple Independent Variables 174
8.2 Analysis of Covariance Structures 175
8.2.1 Description of Model 175
8.2.2 Estimation 177
8.2.3 Model Fit 180
8.2.4 Test of Significance of Model Parameters 182
8.2.5 Simultaneous Estimation of Measurement Model Parameters with Structural Relationship Parameters Versus Sequential Estimation 183
8.2.6 Identification 183
8.3 Examples 183
8.3.1 Example of Confirmatory Factor Analysis 184
8.3.2 Example of Model to Test Discriminant Validity Between Two Constructs 190
8.3.3 Example of Structural Model with Measurement Models 233
8.4 Assignment 262
References 263
Basic Technical Readings 263
Application Readings 263
9. Analysis of Similarity and Preference Data 265
9.1 Proximity Matrices 265
9.1.1 Metric versus Non-metric Data 265
9.1.2 Unconditional versus Conditional Data 266
9.1.3 Derived Measures of Proximity 266
9.1.4 Alternative Proximity Matrices 266
9.2 Problem Definition 267
9.2.1 Objective Function 268
9.2.2 Stress as an Index of Fit 268
9.2.3 Metric 269
9.2.4 Minimum Number of Stimuli 269
9.2.5 Dimensionality 270
9.2.6 Interpretation of MDS Solution 270
9.2.7 The KYST Algorithm 271
9.3 Individual Differences in Similarity Judgments 272
9.4 Analysis of Preference Data 272
9.4.1 Vector Model of preferences 273
9.4.2 Ideal Point Model of Preference 273
9.5 Examples 273
9.5.1 Example of KYST 274
9.5.2 Example of INDSCAL 278
9.5.3 Example of PROFIT (Property Fitting) Analysis 287
9.5.4 Example of MDPREF 297
9.5.5 Example of PREFMAP 304
9.6 Assignment 318
References 319
Basic Technical Readings 319
Application Readings 319
Appendices 321
Appendix A: Rules in Matrix Algebra 321
Appendix B: Statistical Tables 322
Appendix C: Description of Data Sets 326
Index 341