generalized additive models an introduction with r chapman hall crc texts in statistical science

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Generalized Additive Models

Author : Simon N. Wood
ISBN : 9781498728379
Genre : Mathematics
File Size : 27. 4 MB
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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. Simon N. Wood is a professor of Statistical Science at the University of Bristol, UK, and author of the R package mgcv.

Generalized Additive Models

Author : Simon Wood
ISBN : 9781584884743
Genre : Mathematics
File Size : 22. 9 MB
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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 modelling.

Generalized Additive Models

Author : Simon N. Wood
ISBN : 9781420010404
Genre : Mathematics
File Size : 38. 49 MB
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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 modelling.

Introduction To General And Generalized Linear Models

Author : Henrik Madsen
ISBN : 9781439891148
Genre : Mathematics
File Size : 27. 8 MB
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Bridging the gap between theory and practice for modern statistical model building, Introduction to General and Generalized Linear Models presents likelihood-based techniques for statistical modelling using various types of data. Implementations using R are provided throughout the text, although other software packages are also discussed. Numerous examples show how the problems are solved with R. After describing the necessary likelihood theory, the book covers both general and generalized linear models using the same likelihood-based methods. It presents the corresponding/parallel results for the general linear models first, since they are easier to understand and often more well known. The authors then explore random effects and mixed effects in a Gaussian context. They also introduce non-Gaussian hierarchical models that are members of the exponential family of distributions. Each chapter contains examples and guidelines for solving the problems via R. Providing a flexible framework for data analysis and model building, this text focuses on the statistical methods and models that can help predict the expected value of an outcome, dependent, or response variable. It offers a sound introduction to general and generalized linear models using the popular and powerful likelihood techniques. Ancillary materials are available at www.imm.dtu.dk/~hm/GLM

Linear Models With R

Author : Julian J. Faraway
ISBN : 9780203507278
Genre : Mathematics
File Size : 68. 99 MB
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Books on regression and the analysis of variance abound—many are introductory, many are theoretical. While most of them do serve a purpose, the fact remains that data analysis cannot be properly learned without actually doing it, and this means using a statistical software package. There are many of these to choose from, all with their particular strengths and weaknesses. Lately, however, one such package has begun to rise above the others thanks to its free availability, its versatility as a programming language, and its interactivity. That software is R. In the first book that directly uses R to teach data analysis, Linear Models with R focuses on the practice of regression and analysis of variance. It clearly demonstrates the different methods available and, more importantly, in which situations each one applies. It covers all of the standard topics, from the basics of estimation to missing data, factorial designs, and block designs. It also discusses topics, such as model uncertainty, rarely addressed in books of this type. The presentation incorporates numerous examples that clarify both the use of each technique and the conclusions one can draw from the results. All of the data sets used in the book are available for download from http://people.bath.ac.uk/jjf23/LMR/ The author assumes that readers know the essentials of statistical inference and have a basic knowledge of data analysis, linear algebra, and calculus. The treatment reflects his view of statistical theory and his belief that qualitative statistical concepts, while somewhat more difficult to learn, are just as important because they enable us to practice statistics rather than just talk about it.

An Introduction To Generalized Linear Models Third Edition

Author : Annette J. Dobson
ISBN : 1584889500
Genre : Mathematics
File Size : 21. 19 MB
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Continuing to emphasize numerical and graphical methods, An Introduction to Generalized Linear Models, Third Edition provides a cohesive framework for statistical modeling. This new edition of a bestseller has been updated with Stata, R, and WinBUGS code as well as three new chapters on Bayesian analysis. Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers normal, Poisson, and binomial distributions; linear regression models; classical estimation and model fitting methods; and frequentist methods of statistical inference. After forming this foundation, the authors explore multiple linear regression, analysis of variance (ANOVA), logistic regression, log-linear models, survival analysis, multilevel modeling, Bayesian models, and Markov chain Monte Carlo (MCMC) methods. Using popular statistical software programs, this concise and accessible text illustrates practical approaches to estimation, model fitting, and model comparisons. It includes examples and exercises with complete data sets for nearly all the models covered.

Generalized Additive Models

Author : T.J. Hastie
ISBN : 0412343908
Genre : Mathematics
File Size : 45. 15 MB
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This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods relax the linear assumption of many standard models and allow analysts to uncover structure in the data that might otherwise have been missed. While McCullagh and Nelder's Generalized Linear Models shows how to extend the usual linear methodology to cover analysis of a range of data types, Generalized Additive Models enhances this methodology even further by incorporating the flexibility of nonparametric regression. Clear prose, exercises in each chapter, and case studies enhance this popular text.

Generalized Linear Mixed Models

Author : Walter W. Stroup
ISBN : 9781439815137
Genre : Mathematics
File Size : 30. 74 MB
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Generalized Linear Mixed Models: Modern Concepts, Methods and Applications presents an introduction to linear modeling using the generalized linear mixed model (GLMM) as an overarching conceptual framework. For readers new to linear models, the book helps them see the big picture. It shows how linear models fit with the rest of the core statistics curriculum and points out the major issues that statistical modelers must consider. Along with describing common applications of GLMMs, the text introduces the essential theory and main methodology associated with linear models that accommodate random model effects and non-Gaussian data. Unlike traditional linear model textbooks that focus on normally distributed data, this one adopts a generalized mixed model approach throughout: data for linear modeling need not be normally distributed and effects may be fixed or random. With numerous examples using SAS® PROC GLIMMIX, this book is ideal for graduate students in statistics, statistics professionals seeking to update their knowledge, and researchers new to the generalized linear model thought process. It focuses on data-driven processes and provides context for extending traditional linear model thinking to generalized linear mixed modeling. See Professor Stroup discuss the book.

A Primer On Linear Models

Author : John F. Monahan
ISBN : 1420062042
Genre : Mathematics
File Size : 28. 23 MB
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A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods. With coverage steadily progressing in complexity, the text first provides examples of the general linear model, including multiple regression models, one-way ANOVA, mixed-effects models, and time series models. It then introduces the basic algebra and geometry of the linear least squares problem, before delving into estimability and the Gauss–Markov model. After presenting the statistical tools of hypothesis tests and confidence intervals, the author analyzes mixed models, such as two-way mixed ANOVA, and the multivariate linear model. The appendices review linear algebra fundamentals and results as well as Lagrange multipliers. This book enables complete comprehension of the material by taking a general, unifying approach to the theory, fundamentals, and exact results of linear models.

Graphics For Statistics And Data Analysis With R

Author : Kevin J. Keen
ISBN : 9780429632211
Genre : Mathematics
File Size : 31. 31 MB
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Praise for the First Edition "The main strength of this book is that it provides a unified framework of graphical tools for data analysis, especially for univariate and low-dimensional multivariate data. In addition, it is clearly written in plain language and the inclusion of R code is particularly useful to assist readers’ understanding of the graphical techniques discussed in the book. ... It not only summarises graphical techniques, but it also serves as a practical reference for researchers and graduate students with an interest in data display." -Han Lin Shang,?Journal of Applied Statistics Graphics for Statistics and Data Analysis with R, Second Edition, presents the basic principles of graphical design and applies these principles to engaging examples using the graphics and lattice packages in R. It offers a wide array of modern graphical displays for data visualization and representation. Added in the second edition are coverage of the ggplot2 graphics package, material on human visualization and color rendering in R, on screen, and in print. Features Emphasizes the fundamentals of statistical graphics and best practice guidelines for producing and choosing among graphical displays in R Presents technical details on topics such as: the estimation of quantiles, nonparametric and parametric density estimation; diagnostic plots for the simple linear regression model; polynomial regression, splines, and locally weighted polynomial regression for producing a smooth curve; Trellis graphics for multivariate data Provides downloadable R code and data for figures at www.graphicsforstatistics.com Kevin J. Keen is a Professor of Mathematics and Statistics at the University of Northern British Columbia (Prince George, Canada) and an Accredited Professional StatisticianTM by the Statistical Society of Canada and the American Statistical Association.

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