1 Introduction page 1
1.1 Motivation 1
1.2 Choice Probabilities and Integration 3
1.3 Outline of Book 7
1.4 Topics Not Covered 8
1.5 A Couple of Notes 11
Part I Behavioral Models
2 Properties of Discrete Choice Models 15
2.1 Overview 15
2.2 The Choice Set 15
2.3 Derivation of Choice Probabilities 18
2.4 Specific Models 21
2.5 Identification of Choice Models 23
2.6 Aggregation 33
2.7 Forecasting 36
2.8 Recalibration of Constants 37
3 Logit 38
3.1 Choice Probabilities 38
3.2 The Scale Parameter 44
3.3 Power and Limitations of Logit 46
3.4 Nonlinear Representative Utility 56
3.5 Consumer Surplus 59
3.6 Derivatives and Elasticities 61
3.7 Estimation 64
3.8 Goodness of Fit and Hypothesis Testing 71
3.9 Case Study: Forecasting for a New
Transit System 75
3.10 Derivation of Logit Probabilities 78
v

4 GEV 80
4.1 Introduction 80
4.2 Nested Logit 81
4.3 Three-Level Nested Logit 90
4.4 Overlapping Nests 93
4.5 Heteroskedastic Logit 96
4.6 The GEV Family 97
5 Probit 101
5.1 Choice Probabilities 101
5.2 Identification 104
5.3 Taste Variation 110
5.4 Substitution Patterns and Failure of IIA 112
5.5 Panel Data 114
5.6 Simulation of the Choice Probabilities 118
6 Mixed Logit 138
6.1 Choice Probabilities 138
6.2 Random Coefficients 141
6.3 Error Components 143
6.4 Substitution Patterns 145
6.5 Approximation to Any Random Utility Model 145
6.6 Simulation 148
6.7 Panel Data 149
6.8 Case Study 151
7 Variations on a Theme 155
7.1 Introduction 155
7.2 Stated-Preference and Revealed-Preference Data 156
7.3 Ranked Data 160
7.4 Ordered Responses 163
7.5 Contingent Valuation 168
7.6 Mixed Models 170
7.7 Dynamic Optimization 173
Part II Estimation
8 Numerical Maximization 189
8.1 Motivation 189
8.2 Notation 189
8.3 Algorithms 191
8.4 Convergence Criterion 202
8.5 Local versus Global Maximum 203
8.6 Variance of the Estimates 204
8.7 Information Identity 205

Contents vii
9 Drawing from Densities 208
9.1 Introduction 208
9.2 Random Draws 208
9.3 Variance Reduction 217
10 Simulation-Assisted Estimation 240
10.1 Motivation 240
10.2 Definition of Estimators 241
10.3 The Central Limit Theorem 248
10.4 Properties of Traditional Estimators 250
10.5 Properties of Simulation-Based Estimators 253
10.6 Numerical Solution 260
11 Individual-Level Parameters 262
11.1 Introduction 262
11.2 Derivation of Conditional Distribution 265
11.3 Implications of Estimation of θ 267
11.4 Monte Carlo Illustration 270
11.5 Average Conditional Distribution 272
11.6 Case Study: Choice of Energy Supplier 273
11.7 Discussion 283
12 Bayesian Procedures 285
12.1 Introduction 285
12.2 Overview of Bayesian Concepts 287
12.3 Simulation of the Posterior Mean 294
12.4 Drawing from the Posterior 296
12.5 Posteriors for the Mean and Variance
of a Normal Distribution 297
12.6 Hierarchical Bayes for Mixed Logit 302
12.7 Case Study: Choice of Energy Supplier 308
12.8 Bayesian Procedures for Probit Models 316
Bibliography 319
Index 331
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