Discrete Choice Methods with Simulation

By: Kenneth E. Train

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Paperback | 1 October 2009 | Edition Number 2

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400 Pages

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Revised

Dimensions(cm)
22.86 x 15.24 x 2.26

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This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

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Introduction	p. 1
Motivation	p. 1
Choice Probabilities and Integration	p. 3
Outline of Book	p. 7
A Couple of Notes	p. 8
Behavioral Models
Properties of Discrete Choice Models	p. 11
Overview	p. 11
The Choice Set	p. 11
Derivation of Choice Probabilities	p. 14
Specific Models	p. 17
Identification of Choice Models	p. 19
Aggregation	p. 29
Forecasting	p. 32
Recalibration of Constants	p. 33
Logit	p. 34
Choice Probabilities	p. 34
The Scale Parameter	p. 40
Power and Limitations of Logit	p. 42
Nonlinear Representative Utility	p. 52
Consumer Surplus	p. 55
Derivatives and Elasticities	p. 57
Estimation	p. 60
Goodness of Fit and Hypothesis Testing	p. 67
Case Study: Forecasting for a New Transit System	p. 71
Derivation of Logit Probabilities	p. 74
GEV	p. 76
Introduction	p. 76
Nested Logit	p. 77
Three-Level Nested Logit	p. 86
Overlapping Nests	p. 89
Heteroskedastic Logit	p. 92
The GEV Family	p. 93
Probit	p. 97
Choice Probabilities	p. 97
Identification	p. 100
Taste Variation	p. 106
Substitution Patterns and Failure of IIA	p. 108
Panel Data	p. 110
Simulation of the Choice Probabilities	p. 114
Mixed Logit	p. 134
Choice Probabilities	p. 134
Random Coefficients	p. 137
Error Components	p. 139
Substitution Patterns	p. 141
Approximation to Any Random Utility Model	p. 141
Simulation	p. 144
Panel Data	p. 145
Case Study	p. 147
Variations on a Theme	p. 151
Introduction	p. 151
Stated-Preference and Revealed-Preference Data	p. 152
Ranked Data	p. 156
Ordered Responses	p. 159
Contingent Valuation	p. 164
Mixed Models	p. 166
Dynamic Optimization	p. 169
Estimation
Numerical Maximization	p. 185
Motivation	p. 185
Notation	p. 185
Algorithms	p. 187
Convergence Criterion	p. 198
Local versus Global Maximum	p. 199
Variance of the Estimates	p. 200
Information Identity	p. 202
Drawing from Densities	p. 205
Introduction	p. 205
Random Draws	p. 205
Variance Reduction	p. 214
Simulation-Assisted Estimation	p. 237
Motivation	p. 237
Definition of Estimators	p. 238
The Central Limit Theorem	p. 245
Properties of Traditional Estimators	p. 247
Properties of Simulation-Based Estimators	p. 250
Numerical Solution	p. 257
Individual-Level Parameters	p. 259
Introduction	p. 259
Derivation of Conditional Distribution	p. 262
Implications of Estimation of $$	p. 264
Monte Carlo Illustration	p. 267
Average Conditional Distribution	p. 269
Case Study: Choice of Energy Supplier	p. 270
Discussion	p. 280
Bayesian Procedures	p. 282
Introduction	p. 282
Overview of Bayesian Concepts	p. 284
Simulation of the Posterior Mean	p. 291
Drawing from the Posterior	p. 293
Posteriors for the Mean and Variance of a Normal Distribution	p. 294
Hierarchical Bayes for Mixed Logit	p. 299
Case Study: Choice of Energy Supplier	p. 305
Bayesian Procedures for Probit Models	p. 313
Endogeneity	p. 315
Overview	p. 315
The BLP Approach	p. 318
Supply Side	p. 328
Control Functions	p. 334
Maximum Likelihood Approach	p. 340
Case Study: Consumers' Choice among New Vehicles	p. 342
EM Algorithms	p. 347
Introduction	p. 347
General Procedure	p. 348
Examples of EM Algorithms	p. 355
Case Study: Demand for Hydrogen Cars	p. 365
Bibliography	p. 371
Index	p. 385
Table of Contents provided by Ingram. All Rights Reserved.

Discrete Choice Methods with Simulation

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Paperback

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