Multinomial Probit - 1st Edition - ISBN: 9780122011504, 9781483299341

Multinomial Probit

1st Edition

The Theory and Its Application to Demand Forecasting

Authors: Carlos Daganzo
eBook ISBN: 9781483299341
Imprint: Academic Press
Published Date: 28th December 1979
Page Count: 222
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Table of Contents



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




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.


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© Academic Press 1979
Academic Press
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About the Authors

Carlos Daganzo Author

Affiliations and Expertise

University of California, Berkeley, U.S.A.