Applied Regression Analysis and Generalized Linear Models

Preface About the Author 1. Statistical Models and Social Science 1.1 Statistical Models and Social Reality 1.2 Observation and Experiment 1.3 Populations and Samples I. DATA CRAFT 2. What Is Regression Analysis? 2.1 Preliminaries 2.2 Naive Nonparametric Regression 2.3 Local Averaging 3. Examining Data 3.1 Univariate Displays 3.2 Plotting Bivariate Data 3.3 Plotting Multivariate Data 4. Transforming Data 4.1 The Family of Powers and Roots 4.2 Transforming Skewness 4.3 Transforming Nonlinearity 4.4 Transforming Nonconstant Spread 4.5 Transforming Proportions 4.6 Estimating Transformations as Parameters* II. LINEAR MODELS AND LEAST SQUARES 5. Linear Least-Squares Regression 5.1 Simple Regression 5.2 Multiple Regression 6. Statistical Inference for Regression 6.1 Simple Regression 6.2 Multiple Regression 6.3 Empirical Versus Structural Relations 6.4 Measurement Error in Explanatory Variables* 7. Dummy-Variable Regression 7.1 A Dichotomous Factor 7.2 Polytomous Factors 7.3 Modeling Interactions 8. Analysis of Variance 8.1 One-Way Analysis of Variance 8.2 Two-Way Analysis of Variance 8.3 Higher-Way Analysis of Variance 8.4 Analysis of Covariance 8.5 Linear Contrasts of Means 9. Statistical Theory for Linear Models* 9.1 Linear Models in Matrix Form 9.2 Least-Squares Fit 9.3 Properties of the Least-Squares Estimator 9.4 Statistical Inference for Linear Models 9.5 Multivariate Linear Models 9.6 Random Regressors 9.7 Specification Error 9.8 Instrumental Variables and Two-Stage Least Squares 10. The Vector Geometry of Linear Models* 10.1 Simple Regression 10.2 Multiple Regression 10.3 Estimating the Error Variance 10.4 Analysis-of-Variance Models III. LINEAR-MODEL DIAGNOSTICS 11. Unusual and Influential Data 11.1 Outliers, Leverage, and Influence 11.2 Assessing Leverage: Hat-Values 11.3 Detecting Outliers: Studentized Residuals 11.4 Measuring Influence 11.5 Numerical Cutoffs for Diagnostic Statistics 11.6 Joint Influence 11.7 Should Unusual Data Be Discarded? 11.8 Some Statistical Details* 12. Non-Normality, Nonconstant Error Variance, Nonlinearity 12.1 Non-Normally Distributed Errors 12.2 Nonconstant Error Variance 12.3 Nonlinearity 12.4 Discrete Data 12.5 Maximum-Likelihood Methods* 12.6 Structural Dimension 13. Collinearity and Its Purported Remedies 13.1 Detecting Collinearity 13.2 Coping With Collinearity: No Quick Fix IV. GENERALIZED LINEAR MODELS 14. Logit and Probit Models for Categorical Response Variables 14.1 Models for Dichotomous Data 14.2 Models for Polytomous Data 14.3 Discrete Explanatory Variables and Contingency Tables 15. Generalized Linear Models 15.1 The Structure of Generalized Linear Models 15.2 Generalized Linear Models for Counts 15.3 Statistical Theory for Generalized Linear Models* 15.4 Diagnostics for Generalized Linear Models 15.5 Analyzing Data From Complex Sample Surveys V. EXTENDING LINEAR AND GENERALIZED LINEAR MODELS 16. Time-Series Regression and Generalized Leasr Squares* 16.1 Generalized Least-Squares Estimation 16.2 Serially Correlated Errors 16.3 GLS Estimation With Autocorrelated Errors 16.4 Correcting OLS Inference for Autocorrelated Errors 16.5 Diagnosing Serially Correlated Errors 16.6 Concluding Remarks 17. Nonlinear Regression 17.1 Polynomial Regression 17.2 Piece-wise Polynomials and Regression Splines 17.3 Transformable Nonlinearity 17.4 Nonlinear Least Squares* 18. Nonparametric Regression 18.1 Nonparametric Simple Regression: Scatterplot Smoothing 18.2 Nonparametric Multiple Regression 18.3 Generalized Nonparametric Regression 19. Robust Regression* 19.1 M Estimation 19.2 Bounded-Influence Regression 19.3 Quantile Regression 19.4 Robust Estimation of Generalized Linear Models 19.5 Concluding Remarks 20. Missing Data in Regression Models 20.1 Missing Data Basics 20.2 Traditional Approaches to Missing Data 20.3 Maximum-Likelihood Estimation for Data Missing at Random* 20.4 Bayesian Multiple Imputation 20.5 Selection Bias and Censoring 21. Bootstrapping Regression Models 21.1 Bootstrapping Basics 21.2 Bootstrap Confidence Intervals 21.3 Bootstrapping Regression Models 21.4 Bootstrap Hypothesis Tests* 21.5 Bootstrapping Complex Sampling Designs 21.6 Concluding Remarks 22. Model Selection, Averaging, and Validation 22.1 Model Selection 22.2 Model Averaging* 22.3 Model Validation VI. MIXED-EFFECT MODELS 23. Linear Mixed-Effects Models for Hierarchical and Longitudinal Data 23.1 Hierarchical and Longitudinal Data 23.2 The Linear Mixed-Effects Model 23.3 Modeling Hierarchical Data 23.4 Modeling Longitudinal Data 23.5 Wald Tests for Fixed Effects 23.6 Likelihood-Ratio Tests of Variance and Covariance Components 23.7 Centering Explanatory Variables, Contextual Effects, and Fixed-Effects Models 23.8 BLUPs 23.9 Statistical Details* 24. Generalized Linear and Nonlinear Mixed-Effects Models 24.1 Generalized Linear Mixed Models 24.2 Nonlinear Mixed Models Appendix A References Author Index Subject Index Data Set Index