Multinomial Probit (eBook)

Front Cover 1
Multinomial Probit: The Theory and its Application to Demand Forecasting 4
Copyright Page 5
Table of Contents 8
Dedication 6
Preface 10
Acknowledgments 14
Chapter 1. 
16 
1.1 Demand Forecasting 17
1.2 Disaggregate Demand Models 19
1.3 Random Utility Model Forms 24
1.4 Calibration of Discrete Choice Models 34
1.5 Prediction with Discrete Choice Models 37
1.6 Practical Considerations in Demand Modeling 41
Chapter 2. 
45 
2.1 The Maximum-Likelihood Method 45
2.2 Choice Probability Calculation Methods 56
2.3 Likelihood Evaluation 73
2.4 Maximization Methods and Computer Output Interpretation 76
2.5 Properties of the Log-Likelihood Function 93
2.6 Summary 96
Chapter 3. 
99 
3.1 Model Specification Considerations 99
3.2 Statistical Properties of MNP Estimators 112
3.3 Model Updating 123
3.4 Goodness-of-Fit Measures and Tests 127
3.5 Summary 137
Chapter 4. 
139 
4.1 Two Common Figures of Merit 141
4.2 General Prediction Techniques 150
4.3 Shortcut Prediction Techniques 161
4.4 Prediction of Equilibrium 170
4.5 Calibration Revisited 180
4.6 Summary 183
Chapter 5. 
185 
5.1 Confidence Intervals on the Mean: Binary Models 186
5.2 Confidence Intervals on the Mean: Multinomial Models 198
5.3 Prediction Intervals 203
5.4 Other Considerations 208
5.5 Summary 211
Appendix A: 
213 
Quadratic Function 213
The First and Second Derivatives of a Quadratic Function 213
Quadratic Forms 214
Diagonalization of Symmetric Square Matrices 214
Properties of Definite and Semidefinite Matrices 214
Maxima and Minima of Quadratic Functions 215
Appendix B: 
217 
Appendix C: 
219 
The Standard Normal Distribution and the Logistic Curve 219
The Multivariate Normal Distribution 221
The Chi-Square Distribution 222
The Distribution of Some Quadratic Forms 222
Appendix D: 
225 
Convex Sets and Convex (Concave) Functions 225
Differential Properties of Convex Functions 226
Unimodality of Convex Functions 226
Other Properties of Convex Functions 227
References 228
Index 232