Goodness of Fit in Linear and Qualitative-Choice Models

Description

Contents 1. Introduction 1.1. Goodness-of-fit measures in Econometrics 1.2. R2 in the linear model 1.3. Goodness of fit in qualitative choice models Part I R2 in the linear model 2. The coefficient of determination, a survey 2.1. Introduction 2.2. The linear model, definitions and assumptions 2.3. The coefficient of determination 2.4. R2 and hypothesis testing 2.5. Probability limit, distribution and moments 2.6. Some limitations 2.7. List of properties 3. R2 in the linear model without a constant term 3.1. Introduction 3.2. Barten's R2 3.2.1. Definition and properties 3.2.2. Moments 3.3. The squared sample correlation coefficient of y and ŷ 3.3.1. Definition and properties 3.3.2. Moments 3.4. Comparison 4. R2 in the linear model with nonspherical disturbances 4.1. Introduction 4.2. Model and assumptions 4.3. The transformed model; Buse's R2 4.4. The original model; Barten's R2 and r2 5. R2 in seemingly unrelated regression equations 5.1. Introduction 5.2. Model and assumptions 5.3. Definition and properties of McElroy's R2 5.4. The squared sample correlation coefficient of (Ω⁻¹/²⊗I)y and (Ω⁻¹/²⊗I)ŷ 6. R2 in the instrumental variable model and simultaneous equations 6.1. Introduction 6.2. The instrumental variable model 6.2.1. R2 in the instrumental variable model 6.3. The simultaneous equations system 6.3.1. R2 in a single structural equation 6.3.2. R2 in the complete system Part II Goodness of fit in qualitative choice models 7. The binary choice and multinomial logit model 7.1. Introduction 7.2. The binary choice model 7.3. The multinomial logit model 8. Goodness-of-fit measures in binary choice models 8.1. Introduction 8.2. Efron's R2 8.3. The likelihood ratio index: McFadden's R2 8.4. Miscellaneous measures 8.5. Examples 9. Tests on the distributional assumption 9.1. Introduction 9.2. Tests based on parametric families of distribution functions 9.2.1. Some classes of distributions 9.2.2. Score test based on the Perks class of distributions 9.2.3. Test on the distributional assumption in the multinomial logit model 9.3. Simulation results 9.4. A non-parametric approach: the Nadaraya-Watson estimator 9.4.1. The asymptotic distribution of the supremum absolute deviation 9.4.2. A quadratic functional Appendix 9.A. Calculations for the Perks class of distributions Appendix 9.B. Proof of Theorem 9.1 10. Overall goodness-of-fit tests 10.1. Introduction 10.2. A goodness-of-fit test for the binary choice model based on weighted squared residuals 10.2.1. The asymptotic distribution of Tn 10.2.2. Chi-square test and simulation results 10.3. A goodness-of-fit test for the multinomial logit model based on weighted squared residuals 10.3.1. The asymptotic distribution of Tmn 10.3.2. Chi-square test and empirical examples 10.3.3. The conditional logit model 10.4. A test based on the maximum rank correlation estimator 10.4.1. Hausman's test 10.4.2. Han's maximum rank correlation estimator and the rank estimator Appendix 10.A. Proofs of Theorems 10.1 and 10.2 Appendix 10.B. Proofs of Theorems 10.3 and 10.4 11. Summary and conclusions 11.1. R2 in the linear model 11.2. Goodness of fit in qualitative choice models Appendix Notation References Samenvatting (Summary in Dutch) Author Index Subject Index