An Introduction to Generalized Additive Models with R

An Introduction to Generalized Additive Models with R

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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 more

Product details

  • Hardback | 410 pages
  • 154.94 x 238.76 x 27.94mm | 725.74g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 103 black & white illustrations
  • 1584884746
  • 9781584884743
  • 371,100

Review quote

"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 hispresentation. This book modernizes and complements Hastie and Tibshirani's landmark book on the topic." -- - Professor Brian D. Marx, Louisiana State University, USAshow more

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 Indexshow more

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