## Discrete Choice Methods with SimulationFocusing on the many advances that are made possible by simulation, this book describes the new generation of discrete choice methods. 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. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing. |

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### Contents

Properties of Discrete Choice Models | 15 |

23 Derivation of Choice Probabilities | 18 |

24 Specific Models | 21 |

25 Identification of Choice Models | 23 |

26 Aggregation | 33 |

27 Forecasting | 36 |

28 Recalibration of Constants | 37 |

Logit | 38 |

73 Ranked Data | 160 |

74 Ordered Responses | 163 |

75 Contingent Valuation | 168 |

76 Mixed Models | 170 |

77 Dynamic Optimization | 173 |

Numerical Maximization | 189 |

83 Algorithms | 191 |

84 Convergence Criterion | 202 |

32 The Scale Parameter | 44 |

33 Power and Limitations of Logit | 46 |

34 Nonlinear Representative Utility | 56 |

35 Consumer Surplus | 59 |

36 Derivatives and Elasticities | 61 |

37 Estimation | 64 |

38 Goodness of Fit and Hypothesis Testing | 71 |

Forecasting for a New Transit System | 75 |

310 Derivation of Logit Probabilities | 78 |

GEV | 80 |

42 Nested Logit | 81 |

43 ThreeLevel Nested Logit | 90 |

44 Overlapping Nests | 93 |

45 Heteroskedastic Logit | 96 |

46 The GEV Family | 97 |

Probit | 101 |

52 Identification | 104 |

53 Taste Variation | 110 |

54 Substitution Patterns and Failure of IIA | 112 |

55 Panel Data | 114 |

56 Simulation of the Choice Probabilities | 118 |

Mixed Logit | 138 |

62 Random Coefficients | 141 |

63 Error Components | 143 |

64 Substitution Patterns | 145 |

66 Simulation | 148 |

67 Panel Data | 149 |

68 Case Study | 151 |

Variations on a Theme | 155 |

72 StatedPreference and RevealedPreference Data | 156 |

85 Local versus Global Maximum | 203 |

86 Variance of the Estimates | 204 |

87 Information Identity | 205 |

Drawing from Densities | 208 |

93 Variance Reduction | 217 |

SimulationAssisted Estimation | 240 |

102 Definition of Estimators | 241 |

103 The Central Limit Theorem | 248 |

104 Properties of Traditional Estimators | 250 |

105 Properties of SimulationBased Estimators | 253 |

106 Numerical Solution | 260 |

IndividualLevel Parameters | 262 |

112 Derivation of Conditional Distribution | 265 |

113 Implications of Estimation of Θ | 267 |

114 Monte Carlo Illustration | 270 |

115 Average Conditional Distribution | 272 |

Choice of Energy Supplier | 273 |

117 Discussion | 283 |

12 Bayesian Procedures | 285 |

122 Overview of Bayesian Concepts | 287 |

123 Simulation of the Posterior Mean | 294 |

124 Drawing from the Posterior | 296 |

125 Posteriors for the Mean and Variance of a Normal Distribution | 297 |

126 Hierarchical Bayes for Mixed Logit | 302 |

Choice of Energy Supplier | 308 |

128 Bayesian Procedures for Probit Models | 316 |

319 | |

331 | |

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### Common terms and phrases

approximation asymptotic average Bayesian procedures behavior calculated choice probabilities choice situation Choleski factor choosing alternative conditional distribution Consider consumer surplus convergence correlation covariance matrix customers decision maker derived described discrete choice models elements equation error differences example explanatory variables extreme value distribution Gibbs sampling gradient Halton draws Halton sequence Hessian iid extreme value independent integral iteration labeled likelihood function log-likelihood function logit formula logit probability lognormal maximization maximum likelihood methods MH algorithm mixed logit model mode choice nested logit model normally distributed number of draws observed obtained ordered logit period person population portion of utility posterior distribution probit model properties provides random draws random terms representative utility researcher rises sampling distribution scale of utility score Section simulated probability specified standard deviation standard logit standard normal stated-preference statistic substitution patterns supplier Suppose taking draws tion truncated unobserved factors unobserved portion vector

### Popular passages

Page 329 - Mixed logit models for recreation demand'. in J. Herriges and C. Kling. eds., Valuing Recreation and the Environment. Edward Elgar, Northampton. MA. Train. K. (2000), 'Halton sequences for mixed logit'.