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Start Analyzing a Wide Range of Problems Since the publication of the bestselling, highly recommended first edition, R has considerably expanded both in popularity and in the number of packages available. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Second Edition takes advantage of the greater functionality now available in R and substantially revises and adds several topics. New to the Second Edition Expanded coverage of binary and binomial responses, including proportion responses, quasibinomial and beta regression, and applied considerations regarding these models New sections on Poisson models with dispersion, zero inflated count models, linear discriminant analysis, and sandwich and robust estimation for generalized linear models (GLMs) Revised chapters on random effects and repeated measures that reflect changes in the lme4 package and show how to perform hypothesis testing for the models using other methods New chapter on the Bayesian analysis of mixed effect models that illustrates the use of STAN and presents the approximation method of INLA Revised chapter on generalized linear mixed models to reflect the much richer choice of fitting software now available Updated coverage of splines and confidence bands in the chapter on nonparametric regression New material on random forests for regression and classification Revamped R code throughout, particularly the many plots using the ggplot2 package Revised and expanded exercises with solutions now included Demonstrates the Interplay of Theory and Practice This textbook continues to cover a range of techniques that grow from the linear regression model. It presents three extensions to the linear framework: GLMs, mixed effect models, and nonparametric regression models. The book explains data analysis using real examples and includes all the R commands necessary to reproduce the analyses.

Introduction Binary Response Heart Disease Example Logistic Regression Inference Diagnostics Model Selection Goodness of Fit Estimation Problems Binomial and Proportion Responses Binomial Regression Model Inference Pearson’s χ2 Statistic Overdispersion Quasi-Binomial Beta Regression Variations on Logistic Regression Latent Variables Link Functions Prospective and Retrospective Sampling Prediction and Effective Doses Matched Case-Control Studies Count Regression Poisson Regression Dispersed Poisson Model Rate Models Negative Binomial Zero Inflated Count Models Contingency Tables Two-by-Two Tables Larger Two-Way Tables Correspondence Analysis Matched Pairs Three-Way Contingency Tables Ordinal Variables Multinomial Data Multinomial Logit Model Linear Discriminant Analysis Hierarchical or Nested Responses Ordinal Multinomial Responses Generalized Linear Models GLM Definition Fitting a GLM Hypothesis Tests GLM Diagnostics Sandwich Estimation Robust Estimation Other GLMs Gamma GLM Inverse Gaussian GLM Joint Modeling of the Mean and Dispersion Quasi-Likelihood GLM Tweedie GLM Random Effects Estimation Inference Estimating Random Effects Prediction Diagnostics Blocks as Random Effects Split Plots Nested Effects Crossed Effects Multilevel Models Repeated Measures and Longitudinal Data Longitudinal Data Repeated Measures Multiple Response Multilevel Models Bayesian Mixed Effect Models STAN INLA Discussion Mixed Effect Models for Nonnormal Responses Generalized Linear Mixed Models Inference Binary Response Count Response Generalized Estimating Equations Nonparametric Regression Kernel Estimators Splines Local Polynomials Confidence Bands Wavelets Discussion of Methods Multivariate Predictors Additive Models Modeling Ozone Concentration Additive Models Using mgcv Generalized Additive Models Alternating Conditional Expectations Additivity and Variance Stabilization Generalized Additive Mixed Models Multivariate Adaptive Regression Splines Trees Regression Trees Tree Pruning Random Forests Classification Trees Classification Using Forests Neural Networks Statistical Models as NNs Feed-Forward Neural Network with One Hidden Layer NN Application Conclusion Appendix A: Likelihood Theory Appendix B: About R Bibliography Index

Julian J. Faraway is a professor of statistics in the Department of Mathematical Sciences at the University of Bath. His research focuses on the analysis of functional and shape data with particular application to the modeling of human motion. He earned a PhD in statistics from the University of California, Berkeley.

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