Discrete Choice Analysis
Contents
List of Tables
List of Figures
Series Foreword
Preface
1 Introduction
1.1 The Context of Transportation Demand Forecasting
1.2 The Background of Discrete Choice Analysis
1.3 Transportation Applications of Discrete Choice Analysis
1.4 Outline of the Book
2 Review of the Statistics of Model Estimation
2.1 The Estimation Problem
Model Estimation
2.2 Criteria for Evaluating Estimators
2.3 Small Sample Properties
Distribution of Estimators
Efficiency
Cramér-Rao Bound: Scalar Case
Cramér-Rao Bound: Vector Case
2.4 Asymptotic Properties
Consistency
The Slutsky Theorem
Asymptotic Distributions and Variance
2.5 Methods of Estimation
Maximum Likelihood
Least Squares
2.6 Key Statistical Tests
The Normal, t, and Quasi-t Tests
F Test for Linear Models
The Likelihood Ratio Test
2.7 Summary
Small Sample Properties
Asymptotic Properties
3 Theories of Individual Choice Behavior
3.1 Introduction
3.2 A Framework for Choice Theories
The Decision Maker
The Alternatives
Alternative Attributes
The Decision Rule
3.3 Rational Behavior
3.4 Economic Consumer Theory
3.5 Extensions of Consumer Theory
3.6 Discrete Choice Theory
3.7 Probabilistic Choice Theory
Constant Utility
Random Utility
3.8 Summary
4 Binary Choice Models
4.1 Making Random Utility Theory Operational
Deterministic and Random Utility Components
Specification of the Systematic Component
Specification of the Disturbances
4.2 Common Binary Choice Models
The Linear Probability Model
Binary Probit
Binary Logit
Limiting Cases of the Linear, Probit, and Logit Models
Other Binary Choice Models
4.3 Examples of Binary Choice Models
Lisco\\u0027s Binary Probit Model
Binary Logit Example
4.4 Maximum Likelihood Estimation of Binary Choice Models
General Formulation for Maximum Likelihood Estimation of Binary Choice Models
Computational Aspects of Maximum Likelihood
Application to Specific Binary Models
4.5 Examples of Maximum Likelihood Estimation
Simple Example Revisited
Washington, D.C., Logit Model Revisited
4.6 Other Estimation Methods for Binary Choice Models
Linear Probability Models
Nonlinear Models: Least Squares and Berkson\\u0027s Method
Other Estimation Methods
4.7 Summary
5 Multinomial Choice
5.1 Theory of Multinomial Choice
5.2 The Multinomial Logit Model
Definition of Multinomial Logit
The Gumbel Distribution: Basic Properties
Derivation of Multinomial Logit
Limiting Cases of the Multinomial Logit Model
Linear-in-Paramaters Logit Model
5.3 Properties of Logit
Independence from Irrelevant Alternatives Property (IIA)
Elasticities of Logit
The Incremental MNL Model
5.4 Specification of a Multinomial Logit Model
5.5 Estimation of Multinomial Logit
Maximum Likelihood
Maximum Likelihood for Repeated Observations
Least Squares
Other Estimators
5.6 Example of Estimation Results
5.7 Other Multinomial Choice Models
Random Coefficients Logit
Ordered Logistic
The Generalized Extreme Value (GEV) Model
Multinomial Probit
5.8 Summary
6 Aggregate Forecasting Techniques
6.1 The Problem of Aggregation across Individuals
6.2 Typology of Aggregation Methods
6.3 Description of Aggregation Procedures
Average Individual Procedure
Classification
Statistical Differentials
Explicit Integration
Sample Enumeration
6.4 A Comparison of Methods for Aggregate Forecasting
6.5 Summary
7 Tests and Practical Issues in Developing Discrete Choice Models
7.1 Introduction
7.2 The Art of Model Building
7.3 A Mode Choice Model Example
7.4 Tests of Alternative Specifications of Variables
Informal Tests of the Coefficient Estimates
The Use of the Asymptotic t Test
Confidence Region for Several Parameters Simultaneously
The Use of the Likelihood Ratio Test
The Use of Goodness-of-Fit Measures
Test of Generic Attributes
Tests of Non-Nested Hypotheses
Tests of Nonlinear Specifications
Constrained Estimation
7.5 Tests of the Model Structure
Tests of the HA Assumption
Test of Taste Variations
Test of Heteroscedasticity
7.6 Prediction Tests
Outlier Analysis
Market Segment Prediction Tests
Policy Forecasting Tests
7.7 Summary
8 Theory of Sampling
8.1 Basic Sampling Concepts
8.2 Overview of Common Sampling Strategies
Stratified Random Sampling
Cluster Sampling
Double Sampling
Systematic Sampling
8.3 Sampling Strategies for Discrete Choice Analysis
Simple Random Sampling
General Stratified Sampling
Enriched Sampling
Double Sampling
Other Sampling Strategies
8.4 Estimating Choice Models under Alternative Sampling Strategies
Estimation with Random Samples (Revisited)
Estimation with General Stratified Samples
Estimation with Enriched Samples
Estimation with Double Samples
8.5 Choosing a Sample Design for Discrete Choice Analysis
Theoretical Results
Practical Concerns
8.6 Summary
9 Aggregation and Sampling of Alternatives
9.1 Introduction
9.2 Aggregation of Alternatives
The Concept of Elemental Alternatives
Random Utilities of Aggregate Alternatives
Extreme Value Distribution of Random Utilities
A Logit Model with Aggregate Alternatives
Modeling Choice among Aggregate Alternatives with Unknown Size
9.3 Estimation of Choice Models with a Sample of Alternatives
Conditional Log Likelihood Function for Sampling of Alternatives
Simple Random Sampling of Alternatives
Importance Sampling of Alternatives
9.4 Estimation Results for Three Destination Choice Models
Models of Nonwork Travel for the Paris Region
Model of Work Trips for Maceio
9.5 Summary
10 Models of Multidimensional Choice and the Nested Logit Model
10.1 Multidimensional Choice Sets
10.2 Multidimensional Choice Sets with Shared Observed Attributes: Joint Logit
Marginal Choice Probabilities
Conditional Choice Probabilities
10.3 Multidimensional Choice Models with Shared Unobserved Attributes: Nested Logit
Assumptions of the Nested Logit Model
Marginal Choice Probabilities for Nested Logit
Conditional Choice Probabilities for Nested Logit
Extension of Nested Logit to Higher Dimensions
Other Applications of Nested Logit
10.4 Estimating the Nested Logit Model
10.5 Multidimensional Choice Models with Shared Unobserved Attributes: Multinomial Probit
10.6 Measure of Accessibility
10.7 Derivation of the Nested Logit Model from the Generalized Extreme Value Model
10.8 An Example of a Multidimensional Choice ModelM
Joint Logit Model
Nested Logit Result
Maximum Likelihood Estimation Results
Corrected Upper-Level Standard Errors and One-Step Newton-Raphson Estimates
Conclusions on Example
10.9 Summary
11 Systems of Models
11.1 Introduction
11.2 Issues in Model System Design
Policy Issues and the Domain of the Model System
Computational Environment
Data Resources
Analytical Approaches and Model System Structure
11.3 A System of Urban Travel Demand Models for Metropolitan Region Transportation Planning
Model System Structure
Component Models
Prediction Tests and Application Procedures
11.4 A Short-Range Travel Demand Model System
The Structure of the Model System
Component Models
Sample Enumeration Forecasting
Tests of the Disaggregate Model System
Policy Analysis Results
11.5 Summary
12 Models of Travel Demand: Future Directions
12.1 Introduction
12.2 Components of Travel Demand Modeling Process
12.3 Behavioral Theory
Extension of Choice Sets
Extension of Assumptions about Information
Linking Travel Behavior to Activity Demand
Interactions among Household Members
Choice Set Determination
Development of Intermediate Constructs
12.4 Measurement
Attributes Collected
Sample Sizes and Sampling Strategies
Preference Data
12.5 Statistical Model Structure
Continuous Logit
Truncated Dependent-Variable Models
Models with Mixed Continuous and Discrete Variables
Time-Series Analysis
Discrete Choice Models with Probabilistic Choice Sets
12.6 Estimation
Statistical Tests
Robust Estimation
12.7 Summary
Bibliography
Index
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