Generalized Additive Models

This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques.

Generalized Additive Models

Author: T.J. Hastie

Publisher: Routledge

ISBN: 1351445960

Page: 352

View: 734

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

Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility.

Generalized Additive Models

Author: Simon Wood

Publisher: CRC Press

ISBN: 1584884746

Page: 410

View: 460

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

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 ...

Generalized Additive Models

Author: Simon N. Wood

Publisher: CRC Press

ISBN: 1498728375

Page: 476

View: 101

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

The methodological contribution of this book stands alone and does not require use of the VGAM package. This book presents a statistical framework that expands generalized linear models (GLMs) for regression modelling.

Vector Generalized Linear and Additive Models

Author: Thomas W. Yee

Publisher: Springer

ISBN: 149392818X

Page: 589

View: 729

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.

Automatic L2 Regularization for Multiple Generalized Additive Models

Mots-clés de l'auteur: Empirical Bayes method ; Expectation-maximization algorithm ; Generalized additive model ; High-performance computing ; Laplace approximation ; L2 regularization ; Non-stationary extremes ; Penalized maximum ...

Automatic L2 Regularization for Multiple Generalized Additive Models

Author: Yousra El Bachir

Publisher:

ISBN:

Page: 121

View: 727

Mots-clés de l'auteur: Empirical Bayes method ; Expectation-maximization algorithm ; Generalized additive model ; High-performance computing ; Laplace approximation ; L2 regularization ; Non-stationary extremes ; Penalized maximum likelihood.

Modeling Longitudinal Data with Generalized Additive Models

Single case designs (SCDs) are short time series that assess intervention effects by measuring units repeatedly over time both in the presence and absence of treatment.

Modeling Longitudinal Data with Generalized Additive Models

Author: Kristynn J. Sullivan

Publisher:

ISBN:

Page: 10

View: 849

Single case designs (SCDs) are short time series that assess intervention effects by measuring units repeatedly over time both in the presence and absence of treatment. For a variety of reasons, interest in the statistical analysis and meta-analysis of these designs has been growing in recent years. This paper proposes modeling SCD data with Generalized Additive Models (GAMs), a semi-parametric method from which it is possible to estimate the functional form of trend directly from the data, arguably capturing the true functional form better than ordinary least squares regression methods in which the researcher must decide which functional form to impose on the data. Generalized Additive Models provide a flexible way to model SCD data, allowing the data to inform the researcher both as to whether significant trend or trend treatment interaction exists, as well as which of those terms need nonlinear representations and which can remain linear. Tables and figures are appended.

A Score Test of Homogeneity in Generalized Additive Models for Zero inflated Count Data

Zero-Inflated Poisson (ZIP) models are often used to analyze the count data with excess zeros.

A Score Test of Homogeneity in Generalized Additive Models for Zero inflated Count Data

Author: Gaowei Nian

Publisher:

ISBN:

Page:

View: 937

Zero-Inflated Poisson (ZIP) models are often used to analyze the count data with excess zeros. In the ZIP model, the Poisson mean and the mixing weight are often assumed to depend on covariates through regression technique. In other words, the effect of covariates on Poisson mean or the mixing weight is specified using a proper link function coupled with a linear predictor which is simply a linear combination of unknown regression coefficients and covariates. However, in practice, this predictor may not be linear in regression parameters but curvilinear or nonlinear. Under such situation, a more general and flexible approach should be considered. One popular method in the literature is Zero-Inflated Generalized Additive Models (ZIGAM) which extends the zero-inflated models to incorporate the use of Generalized Additive Models (GAM). These models can accommodate the nonlinear predictor in the link function. For ZIGAM, it is also of interest to conduct inferences for the mixing weight, particularly evaluating whether the mixing weight equals to zero. Many methodologies have been proposed to examine this question, but all of them are developed under classical zero-inflated models rather than ZIGAM. In this report, we propose a generalized score test to evaluate whether the mixing weight is equal to zero under the framework of ZIGAM with Poisson model. Technically, the proposed score test is developed based on a novel transformation for the mixing weight coupled with proportional constraints on ZIGAM, where it assumes that the smooth components of covariates in both the Poisson mean and the mixing weight have proportional relationships. An intensive simulation study indicates that the proposed score test outperforms the other existing tests when the mixing weight and the Poisson mean truly involve a nonlinear predictor. The recreational fisheries data from the Marine Recreational Information Program (MRIP) survey conducted by National Oceanic and Atmospheric Administration (NOAA) are used to illustrate the proposed methodology.

Generalized Additive Mixed Models

1.1.2 Generalized Additive Models In many applications the linear parametric
assumption in the generalized linear model ( 1.3 ) may not be appropriate
because the outcome variable y may depend on the covariates 11 , ... , Ip in a
very ...

Generalized Additive Mixed Models

Author: Daowen Zhang

Publisher:

ISBN:

Page:

View: 378

Analysis of Variance Design and Regression

The book carefully analyzes small data sets by using tools that are easily scaled to big data. The tools also apply to small relevant data sets that are extracted from big data.

Analysis of Variance  Design  and Regression

Author: Ronald Christensen

Publisher: CRC Press

ISBN: 1315362309

Page: 610

View: 922

Analysis of Variance, Design, and Regression: Linear Modeling for Unbalanced Data, Second Edition presents linear structures for modeling data with an emphasis on how to incorporate specific ideas (hypotheses) about the structure of the data into a linear model for the data. The book carefully analyzes small data sets by using tools that are easily scaled to big data. The tools also apply to small relevant data sets that are extracted from big data. New to the Second Edition Reorganized to focus on unbalanced data Reworked balanced analyses using methods for unbalanced data Introductions to nonparametric and lasso regression Introductions to general additive and generalized additive models Examination of homologous factors Unbalanced split plot analyses Extensions to generalized linear models R, Minitab®, and SAS code on the author’s website The text can be used in a variety of courses, including a yearlong graduate course on regression and ANOVA or a data analysis course for upper-division statistics students and graduate students from other fields. It places a strong emphasis on interpreting the range of computer output encountered when dealing with unbalanced data.

Advanced R Statistical Programming and Data Models

This is a must-have guide and reference on using and programming with the R language.

Advanced R Statistical Programming and Data Models

Author: Matt Wiley

Publisher: Apress

ISBN: 1484228723

Page: 638

View: 490

Carry out a variety of advanced statistical analyses including generalized additive models, mixed effects models, multiple imputation, machine learning, and missing data techniques using R. Each chapter starts with conceptual background information about the techniques, includes multiple examples using R to achieve results, and concludes with a case study. Written by Matt and Joshua F. Wiley, Advanced R Statistical Programming and Data Models shows you how to conduct data analysis using the popular R language. You’ll delve into the preconditions or hypothesis for various statistical tests and techniques and work through concrete examples using R for a variety of these next-level analytics. This is a must-have guide and reference on using and programming with the R language. What You’ll Learn Conduct advanced analyses in R including: generalized linear models, generalized additive models, mixed effects models, machine learning, and parallel processing Carry out regression modeling using R data visualization, linear and advanced regression, additive models, survival / time to event analysis Handle machine learning using R including parallel processing, dimension reduction, and feature selection and classification Address missing data using multiple imputation in R Work on factor analysis, generalized linear mixed models, and modeling intraindividual variability Who This Book Is For Working professionals, researchers, or students who are familiar with R and basic statistical techniques such as linear regression and who want to learn how to use R to perform more advanced analytics. Particularly, researchers and data analysts in the social sciences may benefit from these techniques. Additionally, analysts who need parallel processing to speed up analytics are given proven code to reduce time to result(s).

Modern Regression Techniques Using R

These are all tested using a range of real research examples conducted by the authors in every chapter.

Modern Regression Techniques Using R

Author: Daniel B Wright

Publisher: SAGE

ISBN: 1847879020

Page: 204

View: 587

In a way that is refreshingly engaging and readable, Daniel B. Wright and Kamala 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 via the SAGE homepage. 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 using a range of real research examples conducted by the authors in every chapter.

Multi view Learning with Additive Models on Graphs

The corresponding results are provided for the smoothing spline version of the
gam with similar findings . For this version of the additive model it appears that
both the supervised and semi - supervised examples are closer to the true
function ...

Multi view Learning with Additive Models on Graphs

Author: Mark V. Culp

Publisher:

ISBN:

Page:

View: 112