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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.

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.

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
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