Multinomial Probit
The Theory and Its Application to Demand Forecasting
Published on 13. February 1980
Book
Hardback
222 pages
978-0-12-201150-4 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 229 mm
Width: 151 mm
Weight
450 gr
ISBN-13
978-0-12-201150-4 (9780122011504)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
06/2014
Academic Press
€76.95
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Content
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
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