Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models

Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author's treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the data described in the book is available at http://people.bath.ac.uk/jjf23/ELM/ Statisticians need to be familiar with a broad range of ideas and techniques. This book provides a well-stocked toolbox of methodologies, and with its unique presentation of these very modern statistical techniques, holds the potential to break new ground in the way graduate-level courses in this area are taught.

Table of Contents:
INTRODUCTION BINOMIAL DATA Challenger Disaster Example Binomial Regression Model Inference Tolerance Distribution Interpreting Odds Prospective and Retrospective Sampling Choice of Link Function Estimation Problems Goodness of Fit Prediction and Effective Doses Overdispersion Matched Case-Control Studies COUNT REGRESSION Poisson Regression Rate Models Negative Binomial CONTINGENCY TABLES Two-by-Two Tables Larger Two-Way Tables Matched Pairs Three-Way Contingency Tables Ordinal Variables MULTINOMIAL DATA Multinomial Logit Model Hierarchical or Nested Responses Ordinal Multinomial Responses GENERALIZED LINEAR MODELS GLM Definition Fitting a GLM Hypothesis Tests GLM Diagnostics OTHER GLMS Gamma GLM Inverse Gaussian GLM Joint Modeling of the Mean and Dispersion Quasi-Likelihood RANDOM EFFECTS Estimation Inference Predicting Random Effects 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 MIXED EFFECT MODELS FOR NONNORMAL RESPONSES Generalized Linear Mixed Models Generalized Estimating Equations NONPARAMETRIC REGRESSION Kernel Estimators Splines Local Polynomials Wavelets Other Methods Comparison of Methods Multivariate Predictors ADDITIVE MODELS Additive Models Using the gam Package 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 Classification Trees NEURAL NETWORKS Statistical Models as NNs Feed-Forward Neural Network with One Hidden Layer NN Application Conclusion APPENDICES Likelihood Theory R Information Bibliography Index