The first edition of this book has established itself as one of the leading references on generalized additive models (GAMs), and the only book on the topic to be introductory in nature with a wealth of practical examples and software implementation. It is self-contained, providing the necessary background in linear models, linear mixed models, and generalized linear models (GLMs), before presenting a balanced treatment of the theory and applications of GAMs and related models.
The author bases his approach on a framework of penalized regression splines, and while firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of R software helps explain the theory and illustrates the practical application of the methodology. Each chapter contains an extensive set of exercises, with solutions in an appendix or in the book’s R data package gamair, to enable use as a course text or for self-study.
Table of Contents
Linear Mixed Models
Generalized Linear Models
GAMs in Practice: mgcv
Simon N. Wood is a professor of Statistical Science at the University of Bristol, UK, and author of the R package mgcv.
"A well-written book providing in-depth and comprehensive coverage of regression models from linear models through generalized linear and mixed models to generalized additive models. The book stands out by placing weight on geometric intuition and numerically efficient estimation algorithms, but most importantly by providing many worked-through application examples with details on model choice as well as accompanying R-code. Compared to the first edition, many new developments are included, from improved inference in generalized additive models to extensions such as response distributions outside the exponential family. As the book includes many advanced topics and the necessary theory but develops everything from the basics, it will be of interest to statistical researchers and practitioners alike. It will be a handy reference book for anyone using the popular mgcv R package and could also be used as an accompanying textbook for a series of regression courses for graduate or advanced undergraduate students."
—Sonja Greven, Professor, Department of Statistics, Ludwig-Maximilians-Universität München, Munich
"A great book got even better. Simon Wood’s focus on splines for fitting GAMs allows for a seamless integration with mixed effects models and gaussian processes, which enlarges the scope of GAMs considerably. This book and the R software are wonderful contributions to applied statistics and data science."
—Trevor Hastie, Stanford University
"The first edition of Simon Wood’s Generalized Additive Models appeared in 2006 to wide and well-deserved acclaim. Since then the field has progressed considerably; in particular Wood himself has made a stunning array of major advances. In his newly revised text, Wood expertly and engagingly guides the reader from background material on linear and generalized linear models all the way through the latest developments in generalized additive (mixed) models. For anyone seeking an up-to-date treatment of what smooth models can do, this new edition is indispensable."
—Philip Reiss, University of Haifa and New York University
"This excellent and well-written book covers a lot more than "merely" GAMs, with the first few chapters providing a pretty comprehensive guide to regression modelling in general. That is a boon for would-be GAM-users from applied fields such as ecology, who sometimes find themselves plunged into the deep end of statistical modelling (GAMs) without much practice in the shallow end. The presentation in this second edition now puts mixed-effect models up-front alongside generalized linear models, presenting GAMs as the glorious fruit of their union, with smooth terms being random effects. This leads to a coherent and extensible modelling framework throughout, which I would describe as broadly Bayesian but not dogmatically so. There is a quiet but consistent emphasis on sound theoretical underpinnings and computational reliability— valuable in the field of smoothing, where ad hoc approaches have been rife, and where inferential principles need to be stretched hard to handle the types of model that can nowadays be fitted. The extensive examples using the mgcv R package are realistic and not over-simplified, and nicely show when enough work is enough. The theory chapters pack enough in to let an advanced user extend the machinery to broader classes of data (from my own experience); and they contain substantial new material, reflecting 10 more years of practical experience and application-driven development, for example to cope with huge datasets. The tools and the theory covered by this book and its predecessor have certainly been a major influence on my own statistical practice over the last 20 years, and I have no doubt they will continue to be."
— Dr. Mark Bravington, Senior research statistician, CSIRO, Australia
"The new edition substantially differs in many respects from the original edition. There are about 80 more pages adding new important results, which have been derived in the last decade. The central change is that linear mixed models theory is now already discussed very early within the second chapter. This is a clever didactical change because it makes the equivalence of smooth regression and random effect models much clearer. There are now sections on adaptive smoothing, SCOP-splines, or soap film smoothers. There is lots of modified and new material in the last section of the book on GAMs in practice: mgcv. Here you can find the analysis of several new data problems and also a section on functional data analysis. Overall the content of the second edition is now presented such that effective teaching and learning is strongly promoted. For practitioners working with the R library mgcv, this second edition describes at length all the actual issues and possibilities of this powerful set of functions. This book is definitely covering the state-of-the-art in modern smooth modelling. I strongly recommend this new edition due to all the reasons I have mentioned above."
—Herwig Friedl, Graz University of Technology, Austria
"This book is so much more than it says in the title! In addition to being my go-to text for generalized additive models, it provides a very clear and concise introduction to linear models, linear mixed models, generalized linear models and generalized additive mixed models. This is supplemented by accessible appendices laying out key results in maximum likelihood theory and the matrix algebra required for the theory covered in the book.
The first edition of this excellent text is one of the books I consult most frequently, both for teaching and research purposes.This second edition substantially updates and expands the scope and the depth of the book. There is a new chapter on mixed effects models that expands on material in the first edition, more on GLMMs, an extended chapter on Smoothers that includes treatment of Gaussian Markov Random fields, and well-organised solutions to exercises.
If you teach courses on linear models, GLMs, GLMMs, GAMs or GAMMs you will find this book a valuable resource for theoretical material, for illustrative applications, for exercises, and as a guide to using the mgcv package in your course. If you do research that may require any of the above methods, you will find that this book provides an invaluable synthesis of the areas, as well as a reference source for the technical detail of the methods.
I know of very few statistics books that combine such an accessible synthesis of a broad area of statistics with the rigor and detail that allows the reader to understand the intricacies of virtually any aspect of the area. Prof Wood has a rare ability to see both the wood and the trees with incisive clarity."
—Prof. David Borchers, University of St Andrews
"The first edition of this book has been one of the most valuable resources both to get familiar with generalized additive models and their application, but also to get to know more about the underlying theory. In the ten years since the publication of the first edition, not only the mgcv package, but also the underlying theory have made much progress and it is therefore good to see the second edition reflecting both developments and comprising a lot of new and fascinating material. This applies in particular to many novel elements on inference in generalized additive models, e.g. a much extended overview on methods to select the smoothing parameters, but also high level inference via hypothesis testing, p-values or an Akaike information criterion that takes smoothing parameter uncertainty into account. These inferential developments are backed up by additional details on a large number of smooth terms and response distributions that significantly enhance the applicability of (extended) generalized additive models. Clearly, Simon Wood is one of the driving forces of the success of generalized additive models both due to the software he provides and due to his in-depth theoretical investigation of the underlying properties. I am wholeheartedly convinced that this book will find a wide readership and will accompany many researchers and applied scientists when either tipping their toe or diving deeply into the ocean of generalized additive models."
—Thomas Kneib, Georg-August-Universität Göttingen
"With this second edition, it may be safe to say that Simon Wood has made Generalized Additive Models (and its extensions) more accessible to researchers, practitioners, teachers, and students than ever before. One of my very first thoughts when looking at this book was just how lucky students are these days to have books like this one that carefully and intelligibly place such vast, powerful, and flexible modeling tools at their fingertips. His first edition had already "hit the nail on the head," but it is clear that this refined iteration was well-thought out and deliberately executed with sensitivity toward the reader. Like his code, Simon writes his textbook in an uncompromising, sensible, and approachable way. The book’s title is a complete understatement. For one, the first few chapters present a carefully chosen coverage of the (generalized) linear model and modern approaches to (generalized) random effect variants, which —truth be told— is already enough for a very nice stand-alone course. Yet he goes for far more. From the start, the reader finds balance of theory, inference, and application, all while the author earns the reader’s confidence through relevant and important examples using R. In fact, there is an implicit accountability of utility throughout. Case in point: an entire chapter is devoted to "GAMs in Practice." It is such a pleasure to see Simon’s broader approach toward extensions, e.g.: Spatial Smoothing, GAMLSS, functional regression, single-index models, Bayesian perspectives, and more. Just for added value, the appendices provide unique tool boxes, and there are also exercises to bridge teaching efforts."
—Professor Brian D. Marx, Louisiana State University
Praise for the first edition:
“…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), in 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, in 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
"The book has a very wide scope. It presents theory and many examples, complete with R code. A companion package, gamair, contains all of the data and scripts, grouped by chapter. A crucial aspect of smoothing, which gets much attention, is finding good values for penalty parameters. Compared to the first edition, the size of the book has grown by around 20%. The exercises, with solutions, are still there. ...I can really recommend this book. It does not replace the R help file of the package, which is some 300 pages long. Many further practical details are explained there."
-Paul Eilers (NL), ISCB June 2018