generalized additive models

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Generalized Additive Models

Author : Simon N. Wood
ISBN : 9781498728379
Genre : Mathematics
File Size : 32. 42 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 : T.J. Hastie
ISBN : 9781351445962
Genre : Mathematics
File Size : 78. 31 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 Cubic Splines And Penalized Likelihood

Author : STANFORD UNIV CA DEPT OF STATISTICS.
ISBN : OCLC:123324412
Genre :
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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.

Vector Generalized Linear And Additive Models

Author : Thomas W. Yee
ISBN : 9781493928187
Genre : Mathematics
File Size : 87. 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.

Generalized Additive Models For Gigadata Modeling The U K Black Smoke Network Daily Data

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ISBN : OCLC:1021136884
Genre :
File Size : 31. 17 MB
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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.

Applications Of Generalized Additive Models

Author : Miland Joshi
ISBN : OCLC:824175703
Genre :
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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.

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

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ISBN : OCLC:1051951671
Genre :
File Size : 60. 15 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.

Using Delta Generalized Additive Models To Predict Spatial Distributions And Population Abundance Of Juvenile Pink Shrimp In Tampa Bay Florida

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ISBN : OCLC:1016884563
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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.

Fixed And Mobile Sensor Based Generalized Additive Models For Freeway Incident Detection

Author : Kittichai Thanasupsin
ISBN : OCLC:51774681
Genre : Electronic traffic controls
File Size : 36. 38 MB
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Application Of Generalized Additive Models To Butterfly Transect Count Data

Author : P. Rothery
ISBN : OCLC:704108906
Genre :
File Size : 86. 83 MB
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