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Extending the Linear Model with R

Generalized Linear, Mixed Effects and Nonparametric Regression Models

By Julian J. Faraway

Series Editor: Chris Chatfield, Jim Zidek, Martin A. Tanner

Chapman and Hall/CRC – 2005 – 312 pages

Series: Chapman & Hall/CRC Texts in Statistical Science

Purchasing Options:

  • Add to CartHardback: $98.95
    978-1-58488-424-8
    December 19th 2005

Description

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.

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, 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, 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, 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, Zentralblatt Math, 2006, Vol. 1095, No. 21

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

Name: Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models (Hardback)Chapman and Hall/CRC 
Description: By Julian J. FarawaySeries Editor: Chris Chatfield, Jim Zidek, Martin A. Tanner. 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,...
Categories: Statistical Theory & Methods, Statistical Computing, Statistics for the Biological Sciences