Multinomial Probit: The Theory and Its Application to Demand Forecasting

Multinomial Probit: The Theory and Its Application to Demand Forecasting covers the theoretical and practical aspects of the multinomial probit (MNP) model and its relation to other discrete choice models. This text is divided into five chapters and begins with an overview of the disaggregate demand modeling in the transportation field. The subsequent chapters examine the computational aspects of the maximum-likelihood estimation and the statistical aspects of MNP model calibration. These chapters specifically describe the properties of the log-likelihood function and the statistical properties of MNP estimators. These topics are followed by a discussion of the mechanical aspects of the MNP model. The closing chapter examines the errors in the estimation of the true parameter value due to lack of data and how these errors propagate to the final prediction. This book will prove useful to econometricians, engineers, and applied mathematicians.

Table of Contents:
Preface Acknowledgments Chapter 1 An Introduction to Disaggregate Demand Modeling in the Transportation Field 1.1 Demand Forecasting 1.2 Disaggregate Demand Models 1.3 Random Utility Model Forms 1.4 Calibration of Discrete Choice Models 1.5 Prediction with Discrete Choice Models 1.6 Practical Considerations in Demand Modeling Chapter 2 Maximum-Likelihood Estimation: Computational Aspects 2.1 The Maximum-Likelihood Method 2.2 Choice Probability Calculation Methods 2.3 Likelihood Evaluation 2.4 Maximization Methods and Computer Output Interpretation 2.5 Properties of the Log-Likelihood Function 2.6 Summary Chapter 3 Statistical Aspects of Multinomial Probit Model Calibration 3.1 Model Specification Considerations 3.2 Statistical Properties of MNP Estimators 3.3 Model Updating 3.4 Goodness-of-Fit Measures and Tests 3.5 Summary Chapter 4 Prediction: Mechanical Aspects 4.1 Two Common Figures of Merit 4.2 General Prediction Techniques 4.3 Shortcut Prediction Techniques 4.4 Prediction of Equilibrium 4.5 Calibration Revisited 4.6 Summary Chapter 5 The Statistical Interpretation of Predictions 5.1 Confidence Intervals on the Mean: Binary Models 5.2 Confidence Intervals on the Mean: Multinomial Models 5.3 Prediction Intervals 5.4 Other Considerations 5.5 Summary Appendix A Some Properties and Definitions of Matrices, Determinants, and Quadratic Functions Quadratic Function The First and Second Derivatives of a Quadratic Function Quadratic Forms Diagonalization of Symmetric Square Matrices Properties of Definite and Semidefinite Matrices Maxima and Minima of Quadratic Functions Appendix B The Algebra of Expectations with Matrices Appendix C Some Properties of the Multivariate Normal Distribution The Standard Normal Distribution and the Logistic Curve The Multivariate Normal Distribution The Chi-Square Distribution The Distribution of Some Quadratic Forms Appendix D Some Definitions and Properties of Convex and Concave Functions Convex Sets and Convex (Concave) Functions Differential Properties of Convex Functions Unimodality of Convex Functions Other Properties of Convex Functions References Index