Statistical Analysis of Management Data (eBook)

Hubert Gatignon is the Claude Janssen Chaired Professor of Business Administration at INSEAD. He joined INSEAD in 1994 from the Wharton School of the University of Pennsylvania where he was Professor of Marketing. He holds a Ph.D. in Marketing from the University of California, Los Angeles.His research interests involve (1) modeling the factors influencing the adoption and diffusion of innovations and (2) explaining and econometrically measuring how the effects of marketing mix variables change over conditions and over time. His most recent research concerns strategies for entering a market and for defending a brand's position, as well as international marketing strategy.Dr. Gatignon's publications have appeared in Communications Research, International Journal of Research in Marketing, Journal of Business Research, Journal of Consumer Research, Journal of International Business Studies, Journal of Law, Economics and Organization, Journal of Marketing, Journal of Marketing Research, Management Science, Marketing Letters, Marketing Science, Planning Review, and in Strategic Management Journal. He is the author of Statistical Analysis of Management Data and he is also a co-author of MARKSTRAT3: The Strategic Marketing Simulation, ADSTRAT: An Advertising Decision Support System and COMPTRACK: A Competitive Tracking Software. He co-edited The INSEAD-Wharton Alliance on Globalizing: Strategies for Building Successful Global Businesses.Dr. Gatignon is an Associate Editor of the Journal of Marketing Research and he serves on the editorial boards of International Journal of Research in Marketing (he was the Editor-in-Chief from 2000 until 2006), Journal of Business-to-Business Marketing, Journal of Marketing, Journal of the Academy of Marketing Science, Marketing Letters, Marketing Science and Recherche et Applications en Marketing (He was the Editor-in-Chief from 1998 to 2000). He has also served on the editorial board of Journal of International Business Studies and Journal of International Marketing. Dr. Gatignon is on the advisory board of The Quantitative Marketing Network of the Social Sciences Research Network. He has been an Academic Trustee of the Marketing Science Institute from 1998 to 2004 and is now an Academic Trustee at AiMark (Center for Advanced International Marketing Knowledge).

Preface to Second Edition 6
Preface 7
Contents 8
1 Introduction 15
1.1 Overview 15
1.2 Objectives 16
1.2.1 Develop the Student's Knowledge of the Technical Details of Various Techniques for Analyzing Data 16
1.2.2 Expose Students to Applications and ''Hand-On'' Use of Various Computer Programs for Carrying Out Statistical Analyses of Data 16
1.3 Types of Scales 17
1.3.1 Definition of Different Types of Scales 18
1.3.2 The Impact of the Type of Scale on Statistical Analysis 18
1.4 Topics Covered 19
1.5 Pedagogy 20
Bibliography 22
2 Multivariate Normal Distribution 23
2.1 Univariate Normal Distribution 23
2.2 Bivariate Normal Distribution 23
2.3 Generalization to Multivariate Case 25
2.4 Tests About Means 26
2.4.1 Sampling Distribution of Sample Centroids 26
2.4.1.1 Univariate Distribution 26
2.4.1.2 Multivariate Distribution 27
2.4.2 Significance Test: One-Sample Problem 27
2.4.2.1 Univariate Test 27
2.4.2.2 Multivariate Test with Known 28
2.4.2.3 Multivariate Test with Unknown 28
2.4.3 Significance Test: Two-Sample Problem 29
2.4.3.1 Univariate Test 29
2.4.3.2 Multivariate Test 30
2.4.4 Significance Test: K -Sample Problem 31
2.5 Examples Using SAS 33
2.5.1 Test of the Difference Between Two Mean Vectors -- One-Sample Problem 33
2.5.2 Test of the Difference Between Several Mean Vectors -- K-Sample Problem 35
2.6 Assignment 41
Bibliography 42
Basic Technical Readings 42
Application Readings 42
3 Reliability Alpha, Principle Component Analysis,INTbreak and Exploratory Factor Analysis
3.1 Notions of Measurement Theory 43
3.1.1 Definition of a Measure 43
3.1.2 Parallel Measurements 44
3.1.3 Reliability 44
3.1.4 Composite Scales 45
3.1.4.1 Reliability of a Two-Component Scale Reliability 45
3.1.4.2 Generalization to Composite Measurement with K Components 48
3.2 Exploratory Factor Analysis Factor Analysis 48
3.2.1 Axis Rotation 48
3.2.2 Variance-Maximizing Rotations (Eigenvalues and Eigenvectors) 49
3.2.2.1 The Objective 50
3.2.2.2 Properties of Eigenvalues and Eigenvectors 52
3.2.3 Principal Component Analysis (PCA) 53
3.2.3.1 PCA: A Data Reduction Method 53
3.2.3.2 Principal Component Loadings 54
3.2.3.3 PCA vs. Exploratory Factor Analysis 54
3.2.4 Exploratory Factor Analysis (EFA) Factor Analysis 55
3.2.4.1 The Exploratory Factor Analysis Model 56
3.2.4.2 Estimating Commonalities 58
3.2.4.3 Extracting Initial Factors 58
3.2.4.4 Determining the Number of Factors 58
3.2.4.5 Rotation to Terminal Solution 59
3.2.4.6 Factor Loadings Principle Component Analysis Factor Loadings 59
3.2.4.7 Factor Scores 60
3.3 Application Examples Using SAS 61
3.4 Assignment 67
Bibliography 70
Basic Technical Readings 70
Application Readings 71
4 Confirmatory Factor Analysis 72
4.1 Confirmatory Factor Analysis Confirmatory Factor Analysis : A Strong Measurement Model 72
4.2 Estimation 74
4.2.1 Model Fit 75
4.2.1.1 Chi-Square Tests 76
4.2.1.2 Other Goodness-of-Fit Measures 77
4.2.1.3 Modification Indices 78
4.2.2 Test of Significance of Model Parameters 78
4.3 Summary Procedure for Scale Construction 78
4.3.1 Exploratory Factor Analysis Exploratory Factor Analysis 78
4.3.2 Confirmatory Factor Analysis Confirmatory Factor Analysis 79
4.3.3 Reliability Coefficient 79
4.3.4 Discriminant Validity 79
4.3.5 Convergent Validity 79
4.4 Second-Order Confirmatory Factor Analysis 80
4.5 Multi-group Confirmatory Factor Analysis 82
4.6 Application Examples Using LISREL 85
4.6.1 Example of Confirmatory Factor Analysis Confirmatory Factor Analysis 85
4.6.2 Example of Model to Test Discriminant Validity Between Two Constructs 86
4.6.3 Example of Model to Assess the Convergent Validity of a Construct 91
4.6.4 Example of Second-Order Factor Model 111
4.6.5 Example of Multi-group Factor Analysis 127
4.7 Assignment 133
Bibliography 134
Basic Technical Readings 134
Application Readings 134
5 Multiple Regression with a Single Dependent Variable 136
5.1 Statistical Inference: Least Squares and Maximum Likelihood 136
5.1.1 The Linear Statistical Model 136
5.1.1.1 Error Structure 137
5.1.2 Point Estimation 138
5.1.2.1 OLS Estimator Ordinary Least Squares OLS 138
5.1.2.2 GLS or Aitken Estimator Generalized Least Squares GLS 139
5.1.3 Maximum Likelihood Estimation 140
5.1.4 Properties of Estimator 142
5.1.4.1 Unbiasedness 142
5.1.4.2 Best Linear Estimator 142
5.1.4.3 Summary of Properties 146
5.1.5 R-Squared as a Measure of Fit 146
5.1.5.1 Normal Case of Homoscedasticity 146
5.1.5.2 Case with Non-scalar Error Covariance Matrix E[ee 0 ]=000 2 I 147
5.2 Pooling Issues 148
5.2.1 Linear Restrictions 148
5.2.1.1 Constrained Estimation 150
5.2.2 Pooling Tests and Dummy Variable Models Pooling Tests 151
5.2.3 Strategy for Pooling Tests Pooling Tests 154
5.3 Examples of Linear Model Estimation with SAS 154
5.4 Assignment 160
Bibliography 160
Basic Technical Readings 160
Application Readings 160
6 System of Equations 163
6.1 Seemingly Unrelated Regression (SUR) 163
6.1.1 Set of Equations with Contemporaneously Correlated Disturbances Seemingly Unrelated Regression SUR 163
6.1.2 Estimation 165
6.1.3 Special Cases 167
6.2 A System of Simultaneous Equations 167
6.2.1 The Problem 167
6.2.2 Two-Stage Least Squares: 2SLS Two Stage Least Squares 2SLS 171
6.2.3 Three-Stage Least Squares: 3SLS Three Stage Least Squares 3SLS 172
6.3 Simultaneity and Identification 172
6.3.1 The Problem 172
6.3.2 Order and Rank Conditions 173
6.3.2.1 Order Condition 173
6.3.2.2 Rank Condition 174
6.4 Summary 175
6.4.1 Structure of Matrix 175
6.4.2 Structure of Matrix 175
6.4.3 Test of Covariance Matrix 176
6.4.3.1 Bartlett's Test 176
6.4.3.2 Lawley's Approximation 177
6.4.4 3SLS Versus 2SLS 177
6.5 Examples Using SAS 177
6.5.1 Seemingly Unrelated Regression Example Seemingly Unrelated Regression SUR 177
6.5.2 Two-Stage Least Squares Example Two Stage Least Squares 2SLS 188
6.5.3 Three-Stage Least Squares Example Three Stage Least Squares 3SLS 188
6.6 Assignment 192
Bibliography 196
Basic Technical Readings 196
Application Readings 196
7 Canonical Correlation Analysis 198
7.1 The Method 198
7.1.1 Canonical Loadings 201
7.1.2 Canonical Redundancy Analysis 201
7.2 Testing the Significance of the Canonical Correlations 201
7.3 Multiple Regression as a Special Case of Canonical Correlation Analysis 203
7.4 Examples Using SAS 204
7.5 Assignment 209
Bibliography 209
Application Readings 209
8 Categorical Dependent Variables 210
8.1 Discriminant Analysis Discriminant Analysis 210
8.1.1 The Discriminant Criterion 210
8.1.2 Discriminant Function Discriminant function 213
8.1.2.1 Special Case of K = 2 214
8.1.2.2 Testing the Significance of the Discriminant Solutions 214
8.1.3 Classification and Fit 215
8.1.3.1 Classification 215
8.1.3.2 Measures of Fit 217
8.2 Quantal Choice Models 219
8.2.1 The Difficulties of the Standard Regression Model with Categorical Dependent Variables 219
8.2.2 Transformational Logit Logit 220
8.2.2.1 Resolving the Efficiency Problem 220
8.2.2.2 Resolving the Range Constraint Problem 222
8.2.3 Conditional Logit Model Logit 223
8.2.3.1 Conditional Logit 0 Case 1 (or Discrete Choice in LIMDEP) Logit 224
8.2.3.2 Conditional Logit 0 Case 2 Logit 226
8.2.4 Fit Measures 226
8.2.4.1 Classification Table 227
8.2.4.2 Statistics of Fit 227
8.3 Examples 228
8.3.1 Example of Discriminant Analysis Using SAS Discriminant Analysis 228
8.3.2 Example of Multinomial Logit 0 Case 1 Analysis Using LIMDEP Logit 234
8.3.3 Example of Multinomial Logit -- Case 2 Analysis Using LIMDEP 236
8.4 Assignment 238
Bibliography 238
Basic Technical Readings 238
Application Readings 239
9 Rank-Ordered Data 241
9.1 Conjoint Analysis MONANOVA Conjoint Analysis MONANOVA 241
9.1.1 Effect Coding Versus Dummy Variable Coding 241
9.1.1.1 Effect Coding 244
9.1.1.2 Effect Coding with Two Levels 244
9.1.1.3 Dummy Variable 246
9.1.1.4 Decomposing the Effects in a Regression Model 247
9.1.1.5 Comparing Effect Coding and Dummy Coding 248
9.1.2 Design Programs 248
9.1.3 Estimation of Part-Worth Coefficients 248
9.1.3.1 MONANOVA MONANOVA 248
9.1.3.2 OLS Estimation Ordinary Least Squares OLS 249
9.2 Ordered Probit 249
9.3 Examples 253
9.3.1 Example of MONANOVA Using PC-MDS MONANOVA 253
9.3.2 Example of Conjoint Analysis Using SAS Conjoint Analysis 254
9.3.3 Example of Ordered Probit Analysis Using LIMDEP Probit Ordered Probit 256
9.4 Assignment 258
Bibliography 260
Basic Technical Readings 260
Application Readings 260
10 Error in Variables Analysis of Covariance Structure 262
10.1 The Impact of Imperfect Measures 262
10.1.1 Effect of Errors-in-Variables 262
10.1.2 Reversed Regression 264
10.1.3 Case with Multiple Independent Variables 265
10.2 Analysis of Covariance Structures 266
10.2.1 Description of Model 266
10.2.2 Estimation 268
10.2.3 Model Fit 271
10.2.4 Test of Significance of Model Parameters 272
10.2.5 Simultaneous Estimation of Measurement Model Parameters with Structural Relationship Parameters Versus Sequential Estimation 272
10.2.6 Identification 272
10.2.7 Special Cases of Analysis of Covariance Structure 273
10.2.7.1 Confirmatory Factor Analysis 273
10.2.7.2 Second-Order Factor Analysis 273
10.2.7.3 Canonical Correlation Analysis Canonical correlation 273
10.3 Analysis of Covariance Structure with Means 275
10.4 Examples of Structural Model with Measurement Models Using LISREL 276
10.5 Assignment 277
Bibliography 300
Basic Technical Readings 300
Application Readings 300
11 Cluster Analysis 303
11.1 The Clustering Methods 303
11.1.1 Similarity Measures 304
11.1.2 The Centroid Method 304
11.1.3 Ward's Method 308
11.1.4 Nonhierarchical Clustering: K -Means Method (FASTCLUS) 313
11.2 Examples Using SAS 314
11.2.1 Example of Clustering with the Centroid Method 314
11.2.2 Example of Clustering with Ward0s Method WARD0S METHOD 318
11.2.3 Example of FASTCLUS 318
11.3 Evaluation and Interpretation of Clustering Results 320
11.3.1 Determining the Number of Clusters 320
11.3.2 Size, Density, and Separation of Clusters 328
11.3.3 Tests of Significance on Other Variables than Those Used to Create Clusters 328
11.3.4 Stability of Results 328
11.4 Assignment 329
Bibliography 329
Basic Technical Readings 329
11.4.0 Application Readings 329
12 Analysis of Similarity and Preference Data 331
12.1 Proximity Matrices 331
12.1.1 Metric Versus Nonmetric Data 331
12.1.2 Unconditional Versus Conditional Data 332
12.1.3 Derived Measures of Proximity 332
12.1.4 Alternative Proximity Matrices 332
12.1.4.1 Symmetric (Half) Matrix -- Missing Diagonal (= 0) 332
12.1.4.2 Nonsymmetric Matrix -- Missing Diagonal (= 0) 333
12.1.4.3 Nonsymmetric Matrix =Diagonal Present (= 0) 333
12.2 Problem Definition 333
12.2.1 Objective Function 334
12.2.2 Stress as an Index of Fit 334
12.2.3 Metric 335
12.2.4 Minimum Number of Stimuli 336
12.2.5 Dimensionality 336
12.2.6 Interpretation of MDS Solution Multidimensional Scaling MDS 336
12.2.7 The KYST Algorithm 337
12.3 Individual Differences in Similarity Similarity Judgments 338
12.4 Analysis of Preference Data 339
12.4.1 Vector Model of Preferences 339
12.4.2 Ideal Point Model of Preferences 339
12.5 Examples Using PC-MDS 340
12.5.1 Example of KYST 340
12.5.2 Example of INDSCAL 343
12.5.3 Example of PROFIT (Property Fitting) Analysis 349
12.5.4 Example of MDPREF 358
12.5.5 Example of PREFMAP 364
12.6 Assignment 366
Bibliography 376
Basic Technical Readings 376
Application Readings 376
13 Appendices 377
Appendix A: Rules in Matrix Algebra 377
Vector and Matrix Differentiation 377
Kronecker Products 377
Determinants 377
Trace 377
Appendix B: Statistical Tables 378
Cumulative Normal Distribution 378
Chi-Squared Distribution 378
F Distribution 379
Appendix C: Description of Data Sets 380
The MARKSTRAT® Environment 381
Competition and Market Structure 381
Marketing Mix Decisions 383
Survey 384
Indup 389
Panel 389
Scan 390
Bibliography 392
About the Author 393
Index 395