Generalized Additive Models

An Introduction with R

Author: Simon Wood

Publisher: CRC Press

ISBN: 1584884746

Category: Mathematics

Page: 410

View: 2257

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: T.J. Hastie

Publisher: Routledge

ISBN: 1351445960

Category: Mathematics

Page: 352

View: 6247

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 Additive Models

An Introduction with R, Second Edition

Author: Simon N. Wood

Publisher: CRC Press

ISBN: 1498728375

Category: Mathematics

Page: 496

View: 4161

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.

Vector Generalized Linear and Additive Models

With an Implementation in R

Author: Thomas W. Yee

Publisher: Springer

ISBN: 149392818X

Category: Mathematics

Page: 589

View: 5990

This book presents a greatly enlarged statistical framework compared to generalized linear models (GLMs) with which to approach regression modelling. Comprising of about half-a-dozen major classes of statistical models, and fortified with necessary infrastructure to make the models more fully operable, the framework allows analyses based on many semi-traditional applied statistics models to be performed as a coherent whole. Since their advent in 1972, GLMs have unified important distributions under a single umbrella with enormous implications. However, GLMs are not flexible enough to cope with the demands of practical data analysis. And data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family. The methodology here and accompanying software (the extensive VGAM R package) are directed at these limitations and are described comprehensively for the first time in one volume. This book treats distributions and classical models as generalized regression models, and the result is a much broader application base for GLMs and GAMs. The book can be used in senior undergraduate or first-year postgraduate courses on GLMs or categorical data analysis and as a methodology resource for VGAM users. In the second part of the book, the R package VGAM allows readers to grasp immediately applications of the methodology. R code is integrated in the text, and datasets are used throughout. Potential applications include ecology, finance, biostatistics, and social sciences. The methodological contribution of this book stands alone and does not require use of the VGAM package.

Predictive Modeling Applications in Actuarial Science: Volume 1, Predictive Modeling Techniques

Author: Edward W. Frees,Richard A. Derrig,Glenn Meyers

Publisher: Cambridge University Press

ISBN: 1139992317

Category: Business & Economics

Page: N.A

View: 7977

Predictive modeling involves the use of data to forecast future events. It relies on capturing relationships between explanatory variables and the predicted variables from past occurrences and exploiting this to predict future outcomes. Forecasting future financial events is a core actuarial skill - actuaries routinely apply predictive-modeling techniques in insurance and other risk-management applications. This book is for actuaries and other financial analysts who are developing their expertise in statistics and wish to become familiar with concrete examples of predictive modeling. The book also addresses the needs of more seasoned practising analysts who would like an overview of advanced statistical topics that are particularly relevant in actuarial practice. Predictive Modeling Applications in Actuarial Science emphasizes lifelong learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used by analysts to gain a competitive advantage in situations with complex data.

Analyzing Medical Data Using S-PLUS

Author: Brian Everitt,Sophia Rabe-Hesketh

Publisher: Springer Science & Business Media

ISBN: 1475732856

Category: Computers

Page: 486

View: 3477

Each chapter consists of basic statistical theory, simple examples of S-PLUS code, plus more complex examples of S-PLUS code, and exercises. All data sets are taken from genuine medical investigations and will be available on a web site. The examples in the book contain extensive graphical analysis to highlight one of the prime features of S-PLUS. Written with few details of S-PLUS and less technical descriptions, the book concentrates solely on medical data sets, demonstrating the flexibility of S-PLUS and its huge advantages, particularly for applied medical statisticians.

Non-Life Insurance Pricing with Generalized Linear Models

Author: Esbjörn Ohlsson,Björn Johansson

Publisher: Springer Science & Business Media

ISBN: 9783642107917

Category: Mathematics

Page: 174

View: 1757

Non-life insurance pricing is the art of setting the price of an insurance policy, taking into consideration varoius properties of the insured object and the policy holder. Introduced by British actuaries generalized linear models (GLMs) have become today a the standard aproach for tariff analysis. The book focuses on methods based on GLMs that have been found useful in actuarial practice and provides a set of tools for a tariff analysis. Basic theory of GLMs in a tariff analysis setting is presented with useful extensions of standarde GLM theory that are not in common use. The book meets the European Core Syllabus for actuarial education and is written for actuarial students as well as practicing actuaries. To support reader real data of some complexity are provided at www.math.su.se/GLMbook.

Recent Advances in Functional Data Analysis and Related Topics

Author: Frédéric Ferraty

Publisher: Springer Science & Business Media

ISBN: 9783790827361

Category: Mathematics

Page: 322

View: 7682

New technologies allow us to handle increasingly large datasets, while monitoring devices are becoming ever more sophisticated. This high-tech progress produces statistical units sampled over finer and finer grids. As the measurement points become closer, the data can be considered as observations varying over a continuum. This intrinsic continuous data (called functional data) can be found in various fields of science, including biomechanics, chemometrics, econometrics, environmetrics, geophysics, medicine, etc. The failure of standard multivariate statistics to analyze such functional data has led the statistical community to develop appropriate statistical methodologies, called Functional Data Analysis (FDA). Today, FDA is certainly one of the most motivating and popular statistical topics due to its impact on crucial societal issues (health, environment, etc). This is why the FDA statistical community is rapidly growing, as are the statistical developments . Therefore, it is necessary to organize regular meetings in order to provide a state-of-art review of the recent advances in this fascinating area. This book collects selected and extended papers presented at the second International Workshop of Functional and Operatorial Statistics (Santander, Spain, 16-18 June, 2011), in which many outstanding experts on FDA will present the most relevant advances in this pioneering statistical area. Undoubtedly, these proceedings will be an essential resource for academic researchers, master students, engineers, and practitioners not only in statistics but also in numerous related fields of application.