Document Zbl 1521.62126

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C. W.</a>; <a href="/authors/rippon.paul" title="Author Profile">Rippon, Paul</a>; <a href="/authors/suesse.thomas" title="Author Profile">Suesse, Thomas</a>; <a href="/authors/thas.olivier" title="Author Profile">Thas, Olivier</a></div> <h2 class="title"> <strong>Smooth tests of goodness of fit for the distributional assumption of regression models.</strong> <i>(English)</i> <a class="label nowrap" href="/1521.62126">Zbl 1521.62126</a> </h2> <div class="source"> <a href="/serials/2444" title="Journal Profile">Aust. N. Z. J. Stat.</a> <a href="/?q=in%3A503343" title="Articles in this Issue">64, No. 1, 67-85 (2022)</a>. </div> <div class="abstract">Summary: We focus on regression models that consist of (i) a model for the conditional mean of the outcome and (ii) a distributional assumption about the distribution of the outcome, both conditional on the regressors. Generalised linear models form a well-known example. The choice of the outcome distribution is often motivated by prior or background knowledge of the researcher, or it is simply chosen for convenience. We propose smooth goodness of fit tests for testing the distributional assumption in regression models. The tests arise from embedding the regression model in a smooth family of alternatives, and constructing appropriate score tests that correctly account for nuisance parameter estimation. The tests are customised, focussed and comprehensive. We present several examples to illustrate the wide applicability of our method. A small simulation study demonstrates that our tests have power to detect important deviations from the hypothesised model.</div> <div class="clear"></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%3A62G10" title="MSC2020">62G10</a> </td> <td class="space"> Nonparametric hypothesis testing </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AGLM">GLM</a>; <a href="/?q=ut%3Amodel+diagnostics">model diagnostics</a>; <a href="/?q=ut%3APoisson+regression">Poisson regression</a>; <a href="/?q=ut%3Ascore+test">score test</a>; <a href="/?q=ut%3AZIP+regression">ZIP regression</a></div> <div class="software"> <h3>Software:</h3><a href="/software/11196">gvlma</a>; <a href="/software/26562">COUNT</a>; <a href="/software/41938">DESeq2</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 1521.62126" data-ciurl="/ci/07752712" data-biburl="/bibtex/07752712.bib" data-amsurl="/amsrefs/07752712.bib" data-xmlurl="/xml/07752712.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07752712.pdf" title="Zbl 1521.62126 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/10.1111/anzs.12361" aria-label="DOI for “Smooth tests of goodness of fit for the distributional assumption of regression models”" title="10.1111/anzs.12361">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Anscombe, F. 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