Applied Regression Analysis and Generalized Linear Models

John Fox received a BA from the City College of New York and a PhD from the University of Michigan, both in Sociology. He is Professor Emeritus of Sociology at McMaster University in Hamilton, Ontario, Canada, where he was previously the Senator William McMaster Professor of Social Statistics. Prior to coming to McMaster, he was Professor of Sociology, Professor of Mathematics and Statistics, and Coordinator of the Statistical Consulting Service at York University in Toronto. Professor Fox is the author of many articles and books on applied statistics, including \emph{Applied Regression Analysis and Generalized Linear Models, Third Edition} (Sage, 2016). He is an elected member of the R Foundation, an associate editor of the Journal of Statistical Software, a prior editor of R News and its successor the R Journal, and a prior editor of the Sage Quantitative Applications in the Social Sciences monograph series.

The strength of this text is the unified presentation of several regression topics that provides the student with a global perspective on regression analysis.  The student is well served with this unified approach as it facilitates deeper research on any one topic with more advanced texts.

• PrefaceAbout the Author1. Statistical Models and Social Science1.1 Statistical Models and Social Reality1.2 Observation and Experiment1.3 Populations and SamplesI. DATA CRAFT2. What Is Regression Analysis?2.1 Preliminaries2.2 Naive Nonparametric Regression2.3 Local Averaging3. Examining Data3.1 Univariate Displays3.2 Plotting Bivariate Data3.3 Plotting Multivariate Data4. Transforming Data4.1 The Family of Powers and Roots4.2 Transforming Skewness4.3 Transforming Nonlinearity4.4 Transforming Nonconstant Spread4.5 Transforming Proportions4.6 Estimating Transformations as Parameters*II. LINEAR MODELS AND LEAST SQUARES5. Linear Least-Squares Regression5.1 Simple Regression5.2 Multiple Regression6. Statistical Inference for Regression6.1 Simple Regression6.2 Multiple Regression6.3 Empirical Versus Structural Relations6.4 Measurement Error in Explanatory Variables*7. Dummy-Variable Regression7.1 A Dichotomous Factor7.2 Polytomous Factors7.3 Modeling Interactions8. Analysis of Variance8.1 One-Way Analysis of Variance8.2 Two-Way Analysis of Variance8.3 Higher-Way Analysis of Variance8.4 Analysis of Covariance8.5 Linear Contrasts of Means9. Statistical Theory for Linear Models*9.1 Linear Models in Matrix Form9.2 Least-Squares Fit9.3 Properties of the Least-Squares Estimator9.4 Statistical Inference for Linear Models9.5 Multivariate Linear Models9.6 Random Regressors9.7 Specification Error9.8 Instrumental Variables and Two-Stage Least Squares10. The Vector Geometry of Linear Models*10.1 Simple Regression10.2 Multiple Regression10.3 Estimating the Error Variance10.4 Analysis-of-Variance ModelsIII. LINEAR-MODEL DIAGNOSTICS11. Unusual and Influential Data11.1 Outliers, Leverage, and Influence11.2 Assessing Leverage: Hat-Values11.3 Detecting Outliers: Studentized Residuals11.4 Measuring Influence11.5 Numerical Cutoffs for Diagnostic Statistics11.6 Joint Influence11.7 Should Unusual Data Be Discarded?11.8 Some Statistical Details*12. Non-Normality, Nonconstant Error Variance, Nonlinearity12.1 Non-Normally Distributed Errors12.2 Nonconstant Error Variance12.3 Nonlinearity12.4 Discrete Data12.5 Maximum-Likelihood Methods*12.6 Structural Dimension13. Collinearity and Its Purported Remedies13.1 Detecting Collinearity13.2 Coping With Collinearity: No Quick FixIV. GENERALIZED LINEAR MODELS14. Logit and Probit Models for Categorical Response Variables14.1 Models for Dichotomous Data14.2 Models for Polytomous Data14.3 Discrete Explanatory Variables and Contingency Tables15. Generalized Linear Models15.1 The Structure of Generalized Linear Models15.2 Generalized Linear Models for Counts15.3 Statistical Theory for Generalized Linear Models*15.4 Diagnostics for Generalized Linear Models15.5 Analyzing Data From Complex Sample SurveysV. EXTENDING LINEAR AND GENERALIZED LINEAR MODELS16. Time-Series Regression and Generalized Leasr Squares*16.1 Generalized Least-Squares Estimation16.2 Serially Correlated Errors16.3 GLS Estimation With Autocorrelated Errors16.4 Correcting OLS Inference for Autocorrelated Errors16.5 Diagnosing Serially Correlated Errors16.6 Concluding Remarks17. Nonlinear Regression17.1 Polynomial Regression17.2 Piece-wise Polynomials and Regression Splines17.3 Transformable Nonlinearity17.4 Nonlinear Least Squares*18. Nonparametric Regression18.1 Nonparametric Simple Regression: Scatterplot Smoothing18.2 Nonparametric Multiple Regression18.3 Generalized Nonparametric Regression19. Robust Regression*19.1 M Estimation19.2 Bounded-Influence Regression19.3 Quantile Regression19.4 Robust Estimation of Generalized Linear Models19.5 Concluding Remarks20. Missing Data in Regression Models20.1 Missing Data Basics20.2 Traditional Approaches to Missing Data20.3 Maximum-Likelihood Estimation for Data Missing at Random*20.4 Bayesian Multiple Imputation20.5 Selection Bias and Censoring21. Bootstrapping Regression Models21.1 Bootstrapping Basics21.2 Bootstrap Confidence Intervals21.3 Bootstrapping Regression Models21.4 Bootstrap Hypothesis Tests*21.5 Bootstrapping Complex Sampling Designs21.6 Concluding Remarks22. Model Selection, Averaging, and Validation22.1 Model Selection22.2 Model Averaging*22.3 Model ValidationVI. MIXED-EFFECT MODELS23. Linear Mixed-Effects Models for Hierarchical and Longitudinal Data23.1 Hierarchical and Longitudinal Data23.2 The Linear Mixed-Effects Model23.3 Modeling Hierarchical Data23.4 Modeling Longitudinal Data23.5 Wald Tests for Fixed Effects23.6 Likelihood-Ratio Tests of Variance and Covariance Components23.7 Centering Explanatory Variables, Contextual Effects, and Fixed-Effects Models23.8 BLUPs23.9 Statistical Details*24. Generalized Linear and Nonlinear Mixed-Effects Models24.1 Generalized Linear Mixed Models24.2 Nonlinear Mixed ModelsAppendix AReferencesAuthor IndexSubject IndexData Set Index