generalized additive models

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Generalized Additive Models

Author : Simon Wood
ISBN : 9781584884743
Genre : Mathematics
File Size : 26. 85 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 : T.J. Hastie
ISBN : 9781351445962
Genre : Mathematics
File Size : 66. 56 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 Additive Models

Author : Simon N. Wood
ISBN : 9781498728379
Genre : Mathematics
File Size : 63. 83 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.

Implementing Generalized Additive Models To Estimate The Expected Value Of Sample Information In A Microsimulation Model Results Of Three Case Studies

Author :
ISBN : OCLC:1051951671
Genre :
File Size : 46. 89 MB
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Background. The expected value of sample information (EVSI) can help prioritize research but its application is hampered by computational infeasibility, especially for complex models. We investigated an approach by Strong and colleagues to estimate EVSI by applying generalized additive models (GAM) to results generated from a probabilistic sensitivity analysis (PSA). Methods. For 3 potential HIV prevention and treatment strategies, we estimated life expectancy and lifetime costs using the Cost-effectiveness of Preventing AIDS Complications (CEPAC) model, a complex patient-level microsimulation model of HIV progression. We fitted a GAM—a flexible regression model that estimates the functional form as part of the model fitting process—to the incremental net monetary benefits obtained from the CEPAC PSA. For each case study, we calculated the expected value of partial perfect information (EVPPI) using both the conventional nested Monte Carlo approach and the GAM approach. EVSI was calculated using the GAM approach. Results. For all 3 case studies, the GAM approach consistently gave similar estimates of EVPPI compared with the conventional approach. The EVSI behaved as expected: it increased and converged to EVPPI for larger sample sizes. For each case study, generating the PSA results for the GAM approach required 3 to 4 days on a shared cluster, after which EVPPI and EVSI across a range of sample sizes were evaluated in minutes. The conventional approach required approximately 5 weeks for the EVPPI calculation alone. Conclusion. Estimating EVSI using the GAM approach with results from a PSA dramatically reduced the time required to conduct a computationally intense project, which would otherwise have been impractical. Using the GAM approach, we can efficiently provide policy makers with EVSI estimates, even for complex patient-level microsimulation models.

Generalized Additive Models Cubic Splines And Penalized Likelihood

Author : STANFORD UNIV CA DEPT OF STATISTICS.
ISBN : OCLC:123324412
Genre :
File Size : 52. 58 MB
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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.

Automatic L2 Regularization For Multiple Generalized Additive Models

Author : Yousra El Bachir
ISBN : OCLC:1102059442
Genre :
File Size : 90. 21 MB
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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

Author : Kristynn J. Sullivan
ISBN : OCLC:1066345671
Genre :
File Size : 38. 6 MB
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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.

Generalized Additive Models For Harmonic Regression Analysis

Author : Winterton Jamie Elizabeth
ISBN : OCLC:50420633
Genre :
File Size : 82. 70 MB
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Vector Generalized Linear And Additive Models

Author : Thomas W. Yee
ISBN : 9781493928187
Genre : Mathematics
File Size : 47. 11 MB
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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.

A Beginner S Guide To Generalized Additive Models With R

Author : Alain F. Zuur
ISBN : 0957174128
Genre : Ecology
File Size : 44. 39 MB
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A Beginner's Guide to Generalized Additive Models with R is exclusively available from: www.highstat.com

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