Generalized Additive Models: An Introduction with R
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Summary
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.
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
Editorial 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
