Document Zbl 1431.62308

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Stat. Data Anal.</a> <a href="/?q=in%3A235290" title="Articles in this Issue">50, No. 4, 967-991 (2006)</a>. </div> <div class="abstract">Summary: Generalized additive models (GAM) for modeling nonlinear effects of continuous covariates are now well established tools for the applied statistician. A Bayesian version of GAM’s and extensions to generalized structured additive regression (STAR) are developed. One or two dimensional P-splines are used as the main building block. Inference relies on Markov chain Monte Carlo (MCMC) simulation techniques, and is either based on iteratively weighted least squares (IWLS) proposals or on latent utility representations of (multi)categorical regression models. The approach covers the most common univariate response distributions, e.g., the binomial, Poisson or gamma distribution, as well as multicategorical responses. For the first time, Bayesian semiparametric inference for the widely used multinomial logit model is presented. Two applications on the forest health status of trees and a space-time analysis of health insurance data demonstrate the potential of the approach for realistic modeling of complex problems. Software for the methodology is provided within the public domain package <span class="zbmathjax-textit">BayesX</span>.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6408136">Cited in <strong>101</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62J12" title="MSC2020">62J12</a> </td> <td class="space"> Generalized linear models (logistic models) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62F15" title="MSC2020">62F15</a> </td> <td class="space"> Bayesian inference </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G08" title="MSC2020">62G08</a> </td> <td class="space"> Nonparametric regression and quantile regression </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-08" title="MSC2020">62-08</a> </td> <td class="space"> Computational methods for problems pertaining to statistics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62P10" title="MSC2020">62P10</a> </td> <td class="space"> Applications of statistics to biology and medical sciences; meta analysis </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ageoadditive+models">geoadditive models</a>; <a href="/?q=ut%3AIWLS+proposals">IWLS proposals</a>; <a href="/?q=ut%3Amulticategorical+response">multicategorical response</a>; <a href="/?q=ut%3Astructured+additive+predictors">structured additive predictors</a>; <a href="/?q=ut%3Asurface+smoothing">surface smoothing</a></div> <div class="software"> <h3>Software:</h3><a href="/software/8566">symrcm</a>; <a href="/software/6772">BayesX</a>; <a href="/software/11047">Fahrmeir</a>; <a href="/software/7116">SemiPar</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1431.62308" data-ciurl="/ci/06408136" data-biburl="/bibtex/06408136.bib" data-amsurl="/amsrefs/06408136.bib" data-xmlurl="/xml/06408136.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06408136.pdf" title="Zbl 1431.62308 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.csda.2004.10.011" aria-label="DOI for “Generalized structured additive regression based on Bayesian P-splines”" title="10.1016/j.csda.2004.10.011">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://epub.ub.uni-muenchen.de/1702/" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abe, M., A generalized additive model for discrete-choice data, J. 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