Generalized Additive Models: An Introduction with R

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Overview

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.

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Product Details

Table of 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

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