Bayesian Statistics and Marketing

Peter Rossi is James Collins Distinguished University Professor of Marketing, Economics, and Statistics at the Anderson School of Management, UCLA, USA. He is the author of the popular R package, bayesm, and he has researched and published extensively on pricing and promotion, target marketing, and other related subjects. Greg Allenby is Helen C. Kurtz Professor of Marketing as well as Professor of Statistics at the Fisher College of Business, Ohio State University, USA. He is a Fellow of the Informs Society for Marketing Science and the American Statistical Association, and he has published widely on the development and application of quantitative methods in marketing. Sanjog Misra is Charles H. Kellstadt Professor of Marketing in the Booth School of Business, University of Chicago, USA. He has served as the co-editor of numerous high-impact journals, including Quantiative Marketing and Economics, and his research focuses on the use of machine learning and deep learning to study consumer and firm decisions.

1 Introduction 1

1.1 A Basic Paradigm for Marketing Problems 2

1.2 A Simple Example 3

1.3 Benefits and Costs of the Bayesian Approach 5

1.4 An Overview of Methodological Material and Case Studies 6

1.5 Approximate Bayes Methods and This Book 7

1.6 Computing and This Book 8

2 Bayesian Essentials 11

2.1 Essential Concepts from Distribution Theory 11

2.2 The Goal of Inference and Bayes Theorem 15

2.3 Conditioning and the Likelihood Principle 16

2.4 Prediction and Bayes 17

2.5 Summarizing the Posterior 17

2.6 Decision Theory, Risk, and the Sampling Properties of Bayes Estimators 18

2.7 Identification and Bayesian Inference 20

2.8 Conjugacy, Sufficiency, and Exponential Families 21

2.9 Regression and Multivariate Analysis Examples 23

2.10 Integration and Asymptotic Methods 37

2.11 Importance Sampling 38

2.12 Simulation Primer for Bayesian Problems 42

2.13 Simulation from Posterior of Multivariate Regression Model 47

3 MCMC Methods 49

3.1 MCMC Methods 50

3.2 A Simple Example: Bivariate Normal Gibbs Sampler 52

3.3 Some Markov Chain Theory 57

3.4 Gibbs Sampler 63

3.5 Gibbs Sampler for the SUR Regression Model 64

3.6 Conditional Distributions and Directed Graphs 66

3.7 Hierarchical Linear Models 69

3.8 Data Augmentation and a Probit Example 74

3.9 Mixtures of Normals 78

3.10 Metropolis Algorithms 85

3.11 Metropolis Algorithms Illustrated with the Multinomial Logit Model 92

3.12 Hybrid MCMC Methods 95

3.13 Diagnostics 98

4 Unit-Level Models and Discrete Demand 103

4.1 Latent Variable Models 104

4.2 Multinomial Probit Model 106

4.3 Multivariate Probit Model 116

4.4 Demand Theory and Models Involving Discrete Choice 121

5 Hierarchical Models for Heterogeneous Units 129

5.1 Heterogeneity and Priors 130

5.2 Hierarchical Models 132

5.3 Inference for Hierarchical Models 134

5.4 A Hierarchical Multinomial Logit Example 137

5.5 Using Mixtures of Normals 143

5.6 Further Elaborations of the Normal Model of Heterogeneity 152

5.7 Diagnostic Checks of the First Stage Prior 155

5.8 Findings and Influence on Marketing Practice 156

6 Model Choice and Decision Theory 159

6.1 Model Selection 160

6.2 Bayes Factors in the Conjugate Setting 162

6.3 Asymptotic Methods for Computing Bayes Factors 163

6.4 Computing Bayes Factors Using Importance Sampling 165

6.5 Bayes Factors Using MCMC Draws from the Posterior 166

6.6 Bridge Sampling Methods 169

6.7 Posterior Model Probabilities with Unidentified Parameters 170

6.8 Chib’s Method 171

6.9 An Example of Bayes Factor Computation: Diagonal MNP models 172

6.10 Marketing Decisions and Bayesian Decision Theory 178

6.11 An Example of Bayesian Decision Theory: Valuing Household Purchase Information 180

7 Simultaneity 185

7.1 A Bayesian Approach to Instrumental Variables 186

7.2 Structural Models and Endogeneity/Simultaneity 195

7.3 Non-Random Marketing Mix Variables 200

8 A Bayesian Perspective on Machine Learning 207

8.1 Introduction 207

8.2 Regularization 209

8.3 Bagging 212

8.4 Boosting 216

8.5 Deep Learning 217

8.6 Applications 223

9 Bayesian Analysis for Text Data 227

9.1 Introduction 227

9.2 Consumer Demand 228

9.3 Integrated Models 236

9.4 Discussion 252

10 Case Study 1: Analysis of Choice-Based Conjoint Data Using A Hierarchical Logit Model 255

10.1 Choice-Based Conjoint 255

10.2 A Random Coefficient Logit 258

10.3 Sign Constraints and Priors 258

10.4 The Camera Data 262

10.5 Running the Model 266

10.6 Describing the Draws of Respondent Partworths 268

10.7 Predictive Posteriors 270

10.8 Comparison of Stan and Sawtooth Software to bayesm Routines 273

11 Case Study 2: WTP and Equilibrium Analysis with Conjoint Demand 277

11.1 The Demand for Product Features 278

11.2 Conjoint Surveys and Demand Estimation 282

11.3 WTP Properly Defined 287

11.4 Nash Equilibrium Prices -- Computation and Assumptions 294

11.5 Camera Example 298

12 Case Study 3: Scale Usage Heterogeneity 307

12.1 Background 307

12.2 Model 310

12.3 Priors and MCMC Algorithm 314

12.4 Data 316

12.5 Discussion 320

12.6 R Implementation 322

13 Case Study 4: Volumetric Conjoint 323

13.1 Introduction 323

13.2 Model Development 324

13.3 Estimation 329

13.4 Empirical Analysis 331

13.5 Discussion 339

13.6 Using the Code 342

13.7 Concluding Remarks 342

14 Case Study 5: Approximate Bayes and Personalized Pricing 343

14.1 Heterogeneity and Heterogeneous Treatment Effects 343

14.2 The Framework 344

14.3 Context and Data 345

14.4 Does the Bayesian Bootstrap Work? 346

14.5 A Bayesian Bootstrap Procedure for the HTE Logit 349

14.6 Personalized Pricing 351

Appendix A An Introduction to R and bayesm 357

A.1 Setting up the R Environment and bayesm 357

A.2 The R Language 360

A.3 Using bayesm 379

A.4 Obtaining Help on bayesm 379

A.5 Tips on Using MCMC Methods 381

A.6 Extending and Adapting Our Code 381

References 383

Index 389