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<P>1 Introduction page 1<br>1.1 Motivation 1<br>1.2 Choice Probabilities and Integration 3<br>1.3 Outline of Book 7<br>1.4 Topics Not Covered 8<br>1.5 A Couple of Notes 11<br>Part I Behavioral Models<br>2 Properties of Discrete Choice Models 15<br>2.1 Overview 15<br>2.2 The Choice Set 15<br>2.3 Derivation of Choice Probabilities 18<br>2.4 Specific Models 21<br>2.5 Identification of Choice Models 23<br>2.6 Aggregation 33<br>2.7 Forecasting 36<br>2.8 Recalibration of Constants 37<br>3 Logit 38<br>3.1 Choice Probabilities 38<br>3.2 The Scale Parameter 44<br>3.3 Power and Limitations of Logit 46<br>3.4 Nonlinear Representative Utility 56<br>3.5 Consumer Surplus 59<br>3.6 Derivatives and Elasticities 61<br>3.7 Estimation 64<br>3.8 Goodness of Fit and Hypothesis Testing 71<br>3.9 Case Study: Forecasting for a New<br>Transit System 75<br>3.10 Derivation of Logit Probabilities 78<br>v</P>
<P>4 GEV 80<br>4.1 Introduction 80<br>4.2 Nested Logit 81<br>4.3 Three-Level Nested Logit 90<br>4.4 Overlapping Nests 93<br>4.5 Heteroskedastic Logit 96<br>4.6 The GEV Family 97<br>5 Probit 101<br>5.1 Choice Probabilities 101<br>5.2 Identification 104<br>5.3 Taste Variation 110<br>5.4 Substitution Patterns and Failure of IIA 112<br>5.5 Panel Data 114<br>5.6 Simulation of the Choice Probabilities 118<br>6 Mixed Logit 138<br>6.1 Choice Probabilities 138<br>6.2 Random Coefficients 141<br>6.3 Error Components 143<br>6.4 Substitution Patterns 145<br>6.5 Approximation to Any Random Utility Model 145<br>6.6 Simulation 148<br>6.7 Panel Data 149<br>6.8 Case Study 151<br>7 Variations on a Theme 155<br>7.1 Introduction 155<br>7.2 Stated-Preference and Revealed-Preference Data 156<br>7.3 Ranked Data 160<br>7.4 Ordered Responses 163<br>7.5 Contingent Valuation 168<br>7.6 Mixed Models 170<br>7.7 Dynamic Optimization 173<br>Part II Estimation<br>8 Numerical Maximization 189<br>8.1 Motivation 189<br>8.2 Notation 189<br>8.3 Algorithms 191<br>8.4 Convergence Criterion 202<br>8.5 Local versus Global Maximum 203<br>8.6 Variance of the Estimates 204<br>8.7 Information Identity 205</P>Contents vii<br>9 Drawing from Densities 208<br>9.1 Introduction 208<br>9.2 Random Draws 208<br>9.3 Variance Reduction 217<br>10 Simulation-Assisted Estimation 240<br>10.1 Motivation 240<br>10.2 Definition of Estimators 241<br>10.3 The Central Limit Theorem 248<br>10.4 Properties of Traditional Estimators 250<br>10.5 Properties of Simulation-Based Estimators 253<br>10.6 Numerical Solution 260<br>11 Individual-Level Parameters 262<br>11.1 Introduction 262<br>11.2 Derivation of Conditional Distribution 265<br>11.3 Implications of Estimation of θ 267<br>11.4 Monte Carlo Illustration 270<br>11.5 Average Conditional Distribution 272<br>11.6 Case Study: Choice of Energy Supplier 273<br>11.7 Discussion 283<br>12 Bayesian Procedures 285<br>12.1 Introduction 285<br>12.2 Overview of Bayesian Concepts 287<br>12.3 Simulation of the Posterior Mean 294<br>12.4 Drawing from the Posterior 296<br>12.5 Posteriors for the Mean and Variance<br>of a Normal Distribution 297<br>12.6 Hierarchical Bayes for Mixed Logit 302<br>12.7 Case Study: Choice of Energy Supplier 308<br>12.8 Bayesian Procedures for Probit Models 316<br>Bibliography 319<br>Index 331 <br>[/UseMoney]<br>

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