Extending the Linear Model with R

Generalized Linear, Mixed Effects and Nonparametric Regression Models

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Series: Chapman & Hall/CRC Texts in Statistical Science.

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

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