Foundations of Linear and Generalized Linear Models

ALAN AGRESTI, PhD, is Distinguished Professor Emeritus in the Department of Statistics at the University of Florida. He has presented short courses on generalized linear models and categorical data methods in more than 30 countries. The author of over 200 journal articles, Dr. Agresti is also the author of Categorical Data Analysis, Third Edition, Analysis of Ordinal Categorical Data, Second Edition, and An Introduction to Categorical Data Analysis, Second Edition, all published by Wiley.

• Preface xi1 Introduction to Linear and Generalized Linear Models 11.1 Components of a Generalized Linear Model 21.2 Quantitative/Qualitative Explanatory Variables and Interpreting Effects 61.3 Model Matrices and Model Vector Spaces 101.4 Identifiability and Estimability 131.5 Example: Using Software to Fit a GLM 15Chapter Notes 20Exercises 212 Linear Models: Least Squares Theory 262.1 Least Squares Model Fitting 272.2 Projections of Data Onto Model Spaces 332.3 Linear Model Examples: Projections and SS Decompositions 412.4 Summarizing Variability in a Linear Model 492.5 Residuals Leverage and Influence 562.6 Example: Summarizing the Fit of a Linear Model 622.7 Optimality of Least Squares and Generalized Least Squares 67Chapter Notes 71Exercises 713 Normal Linear Models: Statistical Inference 803.1 Distribution Theory for Normal Variates 813.2 Significance Tests for Normal Linear Models 863.3 Confidence Intervals and Prediction Intervals for Normal Linear Models 953.4 Example: Normal Linear Model Inference 993.5 Multiple Comparisons: Bonferroni Tukey and FDR Methods 107Chapter Notes 111Exercises 1124 Generalized Linear Models: Model Fitting and Inference 1204.1 Exponential Dispersion Family Distributions for a GLM 1204.2 Likelihood and Asymptotic Distributions for GLMs 1234.3 Likelihood-Ratio/Wald/Score Methods of Inference for GLM Parameters 1284.4 Deviance of a GLM Model Comparison and Model Checking 1324.5 Fitting Generalized Linear Models 1384.6 Selecting Explanatory Variables for a GLM 1434.7 Example: Building a GLM 149Appendix: GLM Analogs of Orthogonality Results for Linear Models 156Chapter Notes 158Exercises 1595 Models for Binary Data 1655.1 Link Functions for Binary Data 1655.2 Logistic Regression: Properties and Interpretations 1685.3 Inference About Parameters of Logistic Regression Models 1725.4 Logistic Regression Model Fitting 1765.5 Deviance and Goodness of Fit for Binary GLMs 1795.6 Probit and Complementary Log–Log Models 1835.7 Examples: Binary Data Modeling 186Chapter Notes 193Exercises 1946 Multinomial Response Models 2026.1 Nominal Responses: Baseline-Category Logit Models 2036.2 Ordinal Responses: Cumulative Logit and Probit Models 2096.3 Examples: Nominal and Ordinal Responses 216Chapter Notes 223Exercises 2237 Models for Count Data 2287.1 Poisson GLMs for Counts and Rates 2297.2 Poisson/Multinomial Models for Contingency Tables 2357.3 Negative Binomial GLMS 2477.4 Models for Zero-Inflated Data 2507.5 Example: Modeling Count Data 254Chapter Notes 259Exercises 2608 Quasi-Likelihood Methods 2688.1 Variance Inflation for Overdispersed Poisson and Binomial GLMs 2698.2 Beta-Binomial Models and Quasi-Likelihood Alternatives 2728.3 Quasi-Likelihood and Model Misspecification 278Chapter Notes 282Exercises 2829 Modeling Correlated Responses 2869.1 Marginal Models and Models with Random Effects 2879.2 Normal Linear Mixed Models 2949.3 Fitting and Prediction for Normal Linear Mixed Models 3029.4 Binomial and Poisson GLMMs 3079.5 GLMM Fitting Inference and Prediction 3119.6 Marginal Modeling and Generalized Estimating Equations 3149.7 Example: Modeling Correlated Survey Responses 319Chapter Notes 322Exercises 32410 Bayesian Linear and Generalized Linear Modeling 33310.1 The Bayesian Approach to Statistical Inference 33310.2 Bayesian Linear Models 34010.3 Bayesian Generalized Linear Models 34710.4 Empirical Bayes and Hierarchical Bayes Modeling 351Chapter Notes 357Exercises 35911 Extensions of Generalized Linear Models 36411.1 Robust Regression and Regularization Methods for Fitting Models 36511.2 Modeling With Large p 37511.3 Smoothing Generalized Additive Models and Other GLM Extensions 378Chapter Notes 386Exercises 388Appendix A Supplemental Data Analysis Exercises 391Appendix B Solution Outlines for Selected Exercises 396References 410Author Index 427Example Index 433Subject Index 435

"The book arose from a one-semester graduate level course taught by Alan Agresti at Harvard University. It has a clear didactic focus, which benefits greatly from Agresti’s well-known clear writing style. Each of the 11 chapters is followed by around 40 exercises, which are diverse and interesting.""...I am very happy with the foundational perspective of this book. I think that students who master this material will have a very thorough understanding of the most important aspects of GLMs, which is more valuable than a kaleidoscopic knowledge. This is certainly one of the books I will consider when next I need to teach a course in generalized linear models.""...this is a great introduction to GLMs written in a clear and didactic style, and with a thoughtful choice and presentation of the material. Highly recommended."--Biometrics Journal, 2016"This book is an essential reference for anyone working with or teaching GLMs." (Mathematical Association of America, 2016)