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Generalized Additive Models

Generalized Additive Models Author T.J. Hastie
ISBN-10 9781351445962
Release 2017-10-19
Pages 352
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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 Additive Models

Generalized Additive Models Author Simon N. Wood
ISBN-10 9781498728379
Release 2017-05-18
Pages 496
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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.

Vector Generalized Linear and Additive Models

Vector Generalized Linear and Additive Models Author Thomas W. Yee
ISBN-10 9781493928187
Release 2015-09-11
Pages 589
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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.

The R Book

The R Book Author Michael J. Crawley
ISBN-10 9781118448960
Release 2012-11-07
Pages 1080
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Hugely successful and popular text presenting an extensive and comprehensive guide for all R users The R language is recognized as one of the most powerful and flexible statistical software packages, enabling users to apply many statistical techniques that would be impossible without such software to help implement such large data sets. R has become an essential tool for understanding and carrying out research. This edition: Features full colour text and extensive graphics throughout. Introduces a clear structure with numbered section headings to help readers locate information more efficiently. Looks at the evolution of R over the past five years. Features a new chapter on Bayesian Analysis and Meta-Analysis. Presents a fully revised and updated bibliography and reference section. Is supported by an accompanying website allowing examples from the text to be run by the user. Praise for the first edition: ‘…if you are an R user or wannabe R user, this text is the one that should be on your shelf. The breadth of topics covered is unsurpassed when it comes to texts on data analysis in R.’ (The American Statistician, August 2008) ‘The High-level software language of R is setting standards in quantitative analysis. And now anybody can get to grips with it thanks to The R Book…’ (Professional Pensions, July 2007)

A Beginner s Guide to Generalized Additive Models with R

A Beginner s Guide to Generalized Additive Models with R Author Alain F. Zuur
ISBN-10 0957174128
Release 2012
Pages 188
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A Beginner's Guide to Generalized Additive Models with R is exclusively available from:

Flexible Regression and Smoothing

Flexible Regression and Smoothing Author Mikis D. Stasinopoulos
ISBN-10 9781351980371
Release 2017-04-21
Pages 571
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This book is about learning from data using the Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS extends the Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) to accommodate large complex datasets, which are increasingly prevalent. GAMLSS allows any parametric distribution for the response variable and modelling all the parameters (location, scale and shape) of the distribution as linear or smooth functions of explanatory variables. This book provides a broad overview of GAMLSS methodology and how it is implemented in R. It includes a comprehensive collection of real data examples, integrated code, and figures to illustrate the methods, and is supplemented by a website with code, data and additional materials.

Stochastic Modeling of Scientific Data

Stochastic Modeling of Scientific Data Author Peter Guttorp
ISBN-10 9781351413657
Release 2018-03-29
Pages 384
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Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.

Generalized Additive Models Cubic Splines and Penalized Likelihood

Generalized Additive Models  Cubic Splines and Penalized Likelihood Author STANFORD UNIV CA DEPT OF STATISTICS.
ISBN-10 OCLC:123324412
Release 1987
Pages 20
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Generalized additive models extended the class of generalized linear models by allowing an arbitrary smooth function for any or all of the covariates. The functions are established by the local scoring procedure, using a smoother as a building block in an iterative algorithm. This paper utilizes a cubic spline smoother in the algorithm and show how the resultant procedure can be view as a method for automatically smoothing a suitably defined partial residual, and more formally, a method for maximizing a penalized likelihood. The authors also examine convergence of the inner (backfitting) loop in this case and illustrate these ideas with some binary response data. Keywords: Spline; Non-parametric regression.

Foundations of Linear and Generalized Linear Models

Foundations of Linear and Generalized Linear Models Author Alan Agresti
ISBN-10 9781118730034
Release 2015-02-23
Pages 472
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"This book presents an overview of the foundations and the key ideas and results of linear and generalized linear models under one cover. Written by a prolific academic, researcher, and textbook writer, Foundations of Linear and Generalized Linear Modelsis soon to become the gold standard by which all existing textbooks on the topic will be compared. While the emphasis is clearly and succinctly on theoretical underpinnings, applications in "R" are presented when they help to elucidate the content or promote practical model building. Each chapter contains approximately 15-20 exercises, primarily for readers to practice and extend the theory, but, also to assimilate the ideas by doing some data analysis. The carefully crafted models and examples convey basic concepts and do not get mired down in non-trivial considerations. An author-maintained web site includes, among other numerous pedagogical supplements, analyses that parallel the "R" routines from the book in SAS, SPSS and Stata"--

Using Delta Generalized Additive Models to Predict Spatial Distributions and Population Abundance of Juvenile Pink Shrimp in Tampa Bay Florida

Using Delta Generalized Additive Models to Predict Spatial Distributions and Population Abundance of Juvenile Pink Shrimp in Tampa Bay  Florida Author
ISBN-10 OCLC:1016884563
Release 2016
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Abstract: In this article, we present an approach based on generalized additive models (GAMs) to predict species' distributions and abundance in Florida estuaries with habitat suitability modeling. Environmental data gathered by fisheries-independent monitoring in Tampa Bay from 1998 to 2008 were interpolated to create seasonal habitat maps for temperature, salinity, and dissolved oxygen and annual maps for depth and bottom type. We used delta-GAM models assuming either zero-adjusted gamma or beta-inflated-at-zero distributions to predict catch per unit effort (CPUE) from five habitat variables plus gear type for each estuarine species by life stage and season. Bottom type and gear type were treated as categorical predictors with reference parameterization. Three spline-fitting procedures (the penalized B-spline, cubic smoothing spline, and restricted cubic spline) were applied to the continuous predictors. Two additive, linear submodels on the log and logistic scales were used to predict CPUEs >0 and CPUEs = 0, respectively, across environmental gradients. The best overall model among those estimated was identified based on the lowest Akaike information criterion. A stepwise routine was used to omit continuous predictors that had little predictive power. The model developed was then applied to interpolated habitat data to predict CPUEs across the estuary using GIS. The statistical models, coupled with the use of GIS, provide a method for predicting spatial distributions and population numbers of estuarine species' life stages. An example is presented for juvenile pink shrimp Farfantepenaeus duorarum during the summer in Tampa Bay, Florida. Received February 10, 2015; accepted August 11, 2015.

Generalized Linear Models for Insurance Data

Generalized Linear Models for Insurance Data Author Piet de Jong
ISBN-10 9781139470476
Release 2008-02-28
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This is the only book actuaries need to understand generalized linear models (GLMs) for insurance applications. GLMs are used in the insurance industry to support critical decisions. Until now, no text has introduced GLMs in this context or addressed the problems specific to insurance data. Using insurance data sets, this practical, rigorous book treats GLMs, covers all standard exponential family distributions, extends the methodology to correlated data structures, and discusses recent developments which go beyond the GLM. The issues in the book are specific to insurance data, such as model selection in the presence of large data sets and the handling of varying exposure times. Exercises and data-based practicals help readers to consolidate their skills, with solutions and data sets given on the companion website. Although the book is package-independent, SAS code and output examples feature in an appendix and on the website. In addition, R code and output for all the examples are provided on the website.

Generalized Additive Models for Gigadata Modeling the U K Black Smoke Network Daily Data

Generalized Additive Models for Gigadata  Modeling the U K  Black Smoke Network Daily Data Author
ISBN-10 OCLC:1021136884
Release 2017
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Abstract: We develop scalable methods for fitting penalized regression spline based generalized additive models with of the order of 10 4 coefficients to up to 10 8 data. Computational feasibility rests on: (i) a new iteration scheme for estimation of model coefficients and smoothing parameters, avoiding poorly scaling matrix operations; (ii) parallelization of the iteration's pivoted block Cholesky and basic matrix operations; (iii) the marginal discretization of model covariates to reduce memory footprint, with efficient scalable methods for computing required crossproducts directly from the discrete representation. Marginal discretization enables much finer discretization than joint discretization would permit. We were motivated by the need to model four decades worth of daily particulate data from the U.K. Black Smoke and Sulphur Dioxide Monitoring Network. Although reduced in size recently, over 2000 stations have at some time been part of the network, resulting in some 10 million measurements. Modeling at a daily scale is desirable for accurate trend estimation and mapping, and to provide daily exposure estimates for epidemiological cohort studies. Because of the dataset size, previous work has focused on modeling time or space averaged pollution levels, but this is unsatisfactory from a health perspective, since it is often acute exposure locally and on the time scale of days that is of most importance in driving adverse health outcomes. If computed by conventional means our black smoke model would require a half terabyte of storage just for the model matrix, whereas we are able to compute with it on a desktop workstation. The best previously available reduced memory footprint method would have required three orders of magnitude more computing time than our new method. Supplementary materials for this article are available online.

Nonparametric and Semiparametric Models

Nonparametric and Semiparametric Models Author Wolfgang Härdle
ISBN-10 9783642171468
Release 2012-08-27
Pages 300
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The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.

Generalized Linear Models Second Edition

Generalized Linear Models  Second Edition Author P. McCullagh
ISBN-10 0412317605
Release 1989-08-01
Pages 532
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The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications. The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables. The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions. Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference.

Modern Regression Techniques Using R

Modern Regression Techniques Using R Author Daniel B Wright
ISBN-10 9781446206027
Release 2009-02-19
Pages 216
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Statistics is the language of modern empirical social and behavioural science and the varieties of regression form the basis of this language. Statistical and computing advances have led to new and exciting regressions that have become the necessary tools for any researcher in these fields. In a way that is refreshingly engaging and readable, Wright and London describe the most useful of these techniques and provide step-by-step instructions, using the freeware R, to analyze datasets that can be located on the books' webpage: Techniques covered in this book include multilevel modeling, ANOVA and ANCOVA, path analysis, mediation and moderation, logistic regression (generalized linear models), generalized additive models, and robust methods. These are all tested out using a range of real research examples conducted by the authors in every chapter. Given the wide coverage of techniques, this book will be essential reading for any advanced undergraduate and graduate student (particularly in psychology) and for more experienced researchers wanting to learn how to apply some of the more recent statistical techniques to their datasets. The Authors are donating all royalties from the book to the American Partnership for Eosinophilic Disorders.

Applications of Generalized Additive Models

Applications of Generalized Additive Models Author Miland Joshi
ISBN-10 OCLC:824175703
Release 2011
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Main Purpose The study is primarily a contribution to a question of strategy rather than the development of a new method. It explores the circumstances in which the use of generalized additive models can be recommended. It is thus a contribution to answering the question "When is it a good idea (or not so good an idea) to use GAMs?" Content Following an introductory exposition in which they are compared to generalized linear models, subsequent chapters deal with evidence that could support possible recommendations: 1. A survey of recent studies, in which GAMs have been used and recommended, regarded with greater reserve, or compared to other methods. 2. Original case studies in which the applicability of GAMs is investigated, namely: (a) Receiver operating characteristic curves used in medical diagnostic testing, the associated diagnostic likelihood ratios, and the modelling of the risk score. (b) A study of a possible heat wave effect on mortality in London. (c) Shorter studies, including a study of factors influencing the length of stay in hospital in Queensland, Australia, and a simulation study. 3. Diagnostics, looking in particular at concurvity, and the problems of defining and detecting it. The study ends with recommendations for the use of GAMs, and possible areas for further research. The appendices include a glossary, technical appendices and R code for computations involved in the project.

A Beginner s Guide to R

A Beginner s Guide to R Author Alain Zuur
ISBN-10 0387938370
Release 2009-06-24
Pages 220
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Based on their extensive experience with teaching R and statistics to applied scientists, the authors provide a beginner's guide to R. To avoid the difficulty of teaching R and statistics at the same time, statistical methods are kept to a minimum. The text covers how to download and install R, import and manage data, elementary plotting, an introduction to functions, advanced plotting, and common beginner mistakes. This book contains everything you need to know to get started with R.