Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models
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Summary
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. A supporting Web site at www.stat.lsa.umich.edu/~faraway/ELM holds all of the data described in the book.
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
Editorial Reviews
"…This is a very pleasant book to read. It clearly demonstrates the different methods available and in which situations each one applies. It covers almost all of the standard topics beyond linear models that a graduate student in statistics should know. It also includes discussion of topics such as model diagnostics, rarely addressed in books of this type. The presentation incorporates an abundance of well-chosen examples … In summary, this is book is highly recommended…"
-Biometrics, December 2006
"I enjoyed this text as much as the first one. The book is recommended as a textbook for a computational statistical and data mining course including GLMs and non-parametric regression, and will also be of great value to the applied statistician whose statistical programming environment of choice is R."
– Giovanni Montana, Imperial College, in Journal of Applied Statistics, July 2007, Vol. 34, No. 5
". . . well-written and the discussions are easy to follow . . . very useful as a reference book for applied statisticians and would also serve well as a textbook for students graduating in statistics."
– Andreas Rosenblad, Uppsala University, in Computational Statistics, April 2009, Vol. 24
"The text is well organized and carefully written . . . provides an overview of many modern statistical methodologies and their applications to real data using software. This makes it a useful text for practitioners and graduate students alike."
– Colin Gallagher, Clemson University, in Journal of the American Statistical Association, December 2007, Vol. 102, No. 480
"It provides a well-stocked toolbook of methodologies, and with its unique presentation on these very modern statistical techniques, holds the potential to break new ground in the way graduate-level courses in this area are taught."
– János Sztrik, in Zentralblatt Math, 2006, Vol. 1095, No. 21
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