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Generalized Additive Models

An Introduction with R

By Simon Wood

Series Editor: Chris Chatfield, Jim Zidek, Jim Lindsey

Chapman and Hall/CRC – 2006 – 410 pages

Series: Chapman & Hall/CRC Texts in Statistical Science

Purchasing Options:

  • Add to CartHardback: $104.95
    978-1-58488-474-3
    February 26th 2006

Description

Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility. While Hastie and Tibshirani's outstanding 1990 research monograph on GAMs is largely responsible for this, there has been a long-standing need for an accessible introductory treatment of the subject that also emphasizes recent penalized regression spline approaches to GAMs and the mixed model extensions of these models.

 Generalized Additive Models: An Introduction with R imparts a thorough understanding of the theory and practical applications of GAMs and related advanced models, enabling informed use of these very flexible tools. The author bases his approach on a framework of penalized regression splines, and builds a well-grounded foundation through motivating chapters on linear and generalized linear models. While firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of the freely available R software helps explain the theory and illustrates the practicalities of linear, generalized linear, and generalized additive models, as well as their mixed effect extensions.

The treatment is rich with practical examples, and it includes an entire chapter on the analysis of real data sets using R and the author's add-on package mgcv. Each chapter includes exercises, for which complete solutions are provided in an appendix.

Concise, comprehensive, and essentially self-contained, Generalized Additive Models: An Introduction with R prepares readers with the practical skills and the theoretical background needed to use and understand GAMs and to move on to other GAM-related methods and models, such as SS-ANOVA, P-splines, backfitting and Bayesian approaches to smoothing and additive modelling.

Reviews

“…A strength of this book is the presentation style … . The step-by-step instructions are complemented with clear examples and sample code … . In addition to emphasizing the practical aspects of the methods, a healthy dose of theory helps the reader understand the fundamentals of the underlying approach. The generous use of graphs and plots helps visualization and enhances understanding. … this is an excellent reference book for a broad audience …”

—Christine M. Anderson-Cook (Los Alamos National Laboratory), Journal of the American Statistical Association, June 2007

"This is an amazing book. The title is an understatement. Certainly the book covers an introduction to generalized additive models (GAMs), but to get there, it is almost as if Simon has left no stone unturned. In chapter 1 the usual 'bread and butter' linear models is presented boldly. Chapter 2 continues with an accessible presentation of the generalized linear model that can be used on its own for a separate introductory course. The reader gains confidence, as if anything is possible, and the examples using software puts modern and sophisticated modeling at their fingertips. I was delighted to see the presentation of GAMs uses penalized splines - the author sorts through the clutter and presents a well-chosen toolbox. Chapter 6 brings the smoothing/GAM presentation into contemporary and state-of-the-art light, for one by making the reader aware of relationships among P-splines, mixed models, and Bayesian approaches. The author is careful and clever so that anyone at any level will have new insights from his presentation. This book modernizes and complements Hastie and Tibshirani's landmark book on the topic."

—Professor Brian D. Marx, Louisiana State University, USA

“This attractively written advanced level text shows its style by starting with the question ‘How old is the universe?’. …It serves also as a manual for the author’s mgcv package, which is one of the R’s recommended packages. …The style and emphasis, and the attention to practical data analysis issue, make this a highly appealing volume. …I strongly recommend this book.”

—John Maindonald, Australian National University, Journal of Statistical Software, Vol. 16, July 2006

"In summary, the book is highly accessible and a fascinating read. It meets the author’s aim of providing a fairly full, but concise, theoretical treatment, explaining how the models and methods work. I would recommend it to anyone interested in statistical modelling."

– Weiqi Luo, University of Leeds, in Journal of Applied Statistics, July 2007, Vol. 34, No. 5

Contents

LINEAR MODELS

A simple linear model

Linear models in general

The theory of linear models

The geometry of linear modelling

Practical linear models

Practical modelling with factors

General linear model specification in R

Further linear modelling theory

Exercises

GENERALIZED LINEAR MODELS

The theory of GLMs

Geometry of GLMs

GLMs with R

Likelihood

Exercises

INTRODUCING GAMS

Introduction

Univariate smooth functions

Additive models

Generalized additive models

Summary

Exercises

SOME GAM THEORY

Smoothing bases

Setting up GAMs as penalized GLMs

Justifying P-IRLS

Degrees of freedom and residual variance estimation

Smoothing Parameter Estimation Criteria

Numerical GCV/UBRE: performance iteration

Numerical GCV/UBRE optimization by outer iteration

Distributional results

Confidence interval performance

Further GAM theory

Other approaches to GAMs

Exercises

GAMs IN PRACTICE: mgcv

Cherry trees again

Brain imaging example

Air pollution in Chicago example

Mackerel egg survey example

Portuguese larks example

Other packages

Exercises

MIXED MODELS and GAMMs

Mixed models for balanced data

Linear mixed models in general

Linear mixed models in R

Generalized linear mixed models

GLMMs with R

Generalized additive mixed models

GAMMs with R

Exercises

APPENDICES

A Some matrix algebra

B Solutions to exercises

Bibliography Index

Name: Generalized Additive Models: An Introduction with R (Hardback)Chapman and Hall/CRC 
Description: By Simon WoodSeries Editor: Chris Chatfield, Jim Zidek, Jim Lindsey. Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility. While Hastie and Tibshirani's outstanding 1990 research monograph on GAMs is largely responsible for...
Categories: Regression Analysis and Multivariate Statistics, Statistical Theory & Methods, Statistics for the Biological Sciences, Quantitative Methods