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TOC
1. Alternative Estimators and Sample Design for Discrete Choice Analysis
1.1 Introduction
1.2 The Likelihood of an Observation under Alternative Stratified Sampling Processes
1.3 Estimation of the Choice Model Parameters
1.4 Estimation with p and Q Both Known
1.5 Estimation with p Known and Q Unknown
1.6 Estimation with p Unknown and Q Known
1.7 Estimation with p and Q Both Unknown
1.8 Estimation in a General Stratified Sample
1.9 Selection of a Sample Design and Estimation Method
1.10 Conclusion
2. Efficient Estimation of Discrete-Choice Models
2.1 Introduction
2.2 Discrete Choice Models
2.3 Stratified Sampling and Choice-Based Sampling
2.4 Generalized Choice-Based Sample
2.5 Sample with Known Aggregate Shares
2.6 Aggregate Shares Estimated from an Auxililary Sample
2.7 Supplemented Sample
2.8 General Consideration in Maximum Likelihood Estimation
2.9 Notation for a General Choice-Based Sample
2.10 The Likelihood Function for Choice-Based Samples
2.11 Maximization of the Likelihood
2.12 Asymptotic Properties of the Unconstrained Estimator
2.13 Estimation of Aggregate Shares
2.14 The Unconstrained Maximum Likelihood Estimator
2.15 The Logit Model as a Special Case
2.16 Estimation with Known Aggregate Shares
2.17 Consistency of the Constraint Equations
2.18 Asymptotic Properties with Known Aggregate Shares
2.19 The Constrained Maximum Likelihood Estimator
2.20 Estimation of the Logit Model with Known Aggregate Shares
2.21 Estimation with Aggregate Shares Inferred from an Auxiliary Sample
2.22 Asymptotic Variance of the Auxiliary Sample Estimator
2.24 Estimation with a Supplementary Sample
2.25 Comparison of Estimators and Sample Designs
II Dynamic Discrete Probability Models
3. Statistical Models for Discrete Panel Data
3.1 Introduction
3.2 A Framework for Analyzing Dynamic Choice
3.3 The General Model
3.4 An Independent Trials Bernoulli Model
3.5 A Random Effect Bernoulli Model and One-Factor Schemes
3.6 A Fixed Effect Bernoulli Model
3.7 Models with General Correlation in the Errors : The Concept of Heterogeneity Extended
3.8 Models with Structural State Dependence
3.9 A Renewal Model
3.10 A Model with Habit Persistence
3.11 Computation in the General Model
3.12 A Summary of Section 3.2 through 3.11
3.13 Heterogeneity versus Structural State Dependence : An Application of the Preceeding Models
3.14 Testing for Heterogeneity versus State Dependece
3.15 Analogies with Time-Series Models
3.16 Exampels of Models that Generate Structural State Dependence
3.17 Summary and Conclusion
4. The Incidental Parameters Problem and the Problem of Initial Condition in Estimating a Discrete Time-Discrete Data Stochastic Process
4.1 Introduction
4.2 The Problem of Initial COnditions and Some Formal Solutions
4.3 Simpler Solutions and the Problem of Incidental Parameters
4.4 Some Monte Carlo Evidence
III Structural Discrete Probability Models Derived from Theorities of Choice
5. Econometric Models of Probabilistic Choice
5.1 Economic man
5.2 Discrete Choice
5.3 Probabilistic Consumer Theory
5.4 Probabilistic Choice Systems
5.5 The Random Utility Maximization Hypothesis
5.6 Stochastic Revealed Preference
5.7 Aggregation of Preferences
5.8 The Williams-Daly-Zachary Theorem
5.9 Criteria for Parametric Probabilistic Choice Systems
5.10 Specifications of Variables
5.11 Functional Form
5.12 The Luce Model
5.13 Thurstone’s Model V
5.14 Tversky Elimination Models
5.15 Generalized Extreme Value Models
5.16 Preference Trees
5.17 Estimation of Tree Extreme Value Models
5.18 Sequential Estimation
5.19 An Application
6. Random versus Fixed Coefficient Quantal Choice Models
6.1 Introduction
6.2 Quantal Choice Theory and Variation in Tastes
6.3 An Empirical Comparison of the LPIID and RCCD Models
6.4 Details of the Experiment
6.5 Results
6.6 Analysis of Individual Respondents
6.7 A Comparison of LPIID Probit and RCCD Probit Estimation
7. On the Use of Simulated Frequencies to Approximate Choice Probabilities
7.1 Introduction
7.2 The SImulated Frequency Method
7.3 Bayesian Approach
7.4 Estimation of a Function of a Collection of Probabilities
7.5 Application to the Calculation of Multinomial Probit
7.6 The Simulation Routine
7.7 The Clark Method
7.8 Numerical Test Objecives and Design
7.9 Test Result and Analysis
8. Application of a Continuous Spatial Choice Logit Model
8.1 Introduction
8.2 Basic Definition
8.3 Spatial Aggregation
8.4 The Discrete Logit Model
8.5 Spatial Aggregation Using Continuous Functions
8.6 The Continuous Logit Model
8.7 A Parametric Example of Spatial Aggregation
8.8 Continuous Logit with Featureless Plane
8.9 Basic Operations of the MIT-TRANS Model
IV Simultaneous Equations Models with Discrete Endogenous Variables
9. Simultaneous Equations Models with Discrete and Censored Variables
9.1 Introduction
9.2 Two-Stage Methods and Amemiya’s Principle
9.3 Structural Equations with Probit Structure
9.4 Structural Equations with Observable Continuous Endogenous Variables
9.5 Structural Equations with Censored Dependent Variables
9.6 Structural Equations with Tobit Structure
9.7 Switching and Censored Models with Sample Separation Information
10. Stratification on Endogenous Varables and Estimate The Gary Income Maintenance
Experiment
10.1 Introduction
10.2 The Problem of Endogenous Sampling and Estimation Methods
10.3 Relative Efficiencies of Weighted Least Squares versus Maximum Likelihood Estimates
10.4 Empirical Results of the Selection Bias in the Gary Income Maintenanance Experiment
10.5 Alternative Sampling Procedures
11. A Switching Simultaneous Equations Model of Physician Behavior in Ontario
11.1 Introduction
11.2 Econometric Model
11.3 Estimation
11.4 Estimation of the Switching (Option) Equation
11.5 Empirical Results
11.6 Estimated Options Equation
11.7 Estimated Referral Equation
12. Constraints on the Parameters in Simultaneous Tobit and Probit Models
12.1 Introduction
12.2 Simultaneous Tobit Models
12.3 All Endogenous Variables Truncated
12.4 Some Endogenous Variables Truncated
12.5 Both Y and Y* as Explanatory Variables
12.6 Simultaneous Probit Models
12.7 All Endogenous Variables Truncated
12.8 Some Endogenous Variable Truncated
12.9 Both Y and Y* as Explanatory Variables
13. Estimating Credit COnstraints by Switching Regression
13.1 Introduction
13.2 The Supply of Debt
13.3 The Model and Data
13.4 Simultaneous Switching Regression and Linear Equations
13.5 The Evidence
13.6 Qualifications and Evaluations
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