Document Zbl 1322.62030

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Comput.</a> <a href="/?q=in%3A293989" title="Articles in this Issue">22, No. 1, 121-139 (2012)</a>. </div> <div class="abstract">Summary: Nonlinear mixed-effects models are very useful to analyze repeated measures data and are used in a variety of applications. Normal distributions for random effects and residual errors are usually assumed, but such assumptions make inferences vulnerable to the presence of outliers. In this work, we introduce an extension of a normal nonlinear mixed-effects model considering a subclass of elliptical contoured distributions for both random effects and residual errors. This elliptical subclass, the scale mixtures of normal (SMN) distributions, includes heavy-tailed multivariate distributions, such as Student-$t$, the contaminated normal and slash, among others, and represents an interesting alternative to outliers accommodation maintaining the elegance and simplicity of the maximum likelihood theory. We propose an exact estimation procedure to obtain the maximum likelihood estimates of the fixed-effects and variance components, using a stochastic approximation of the EM algorithm. We compare the performance of the normal and the SMN models with two real data sets.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6495006">Cited in <strong>33</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td class="mono"> 62-07 </td> <td class="space"> Data analysis (statistics) (MSC2010) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62E10" title="MSC2020">62E10</a> </td> <td class="space"> Characterization and structure theory of statistical distributions </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amixed-effects+model">mixed-effects model</a>; <a href="/?q=ut%3Aoutliers">outliers</a>; <a href="/?q=ut%3Ascale+mixtures+of+normal+distributions">scale mixtures of normal distributions</a>; <a href="/?q=ut%3ASAEM+algorithm">SAEM algorithm</a>; <a href="/?q=ut%3Arandom+effects">random effects</a></div> <div class="software"> <h3>Software:</h3><a href="/software/11219">MEMSS</a>; <a href="/software/4492">WinBUGS</a>; <a href="/software/2892">S-PLUS</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 1322.62030" data-ciurl="/ci/06495006" data-biburl="/bibtex/06495006.bib" data-amsurl="/amsrefs/06495006.bib" data-xmlurl="/xml/06495006.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06495006.pdf" title="Zbl 1322.62030 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/10.1007/s11222-010-9212-1" aria-label="DOI for “Estimation in nonlinear mixed-effects models using heavy-tailed distributions”" title="10.1007/s11222-010-9212-1">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">Andrews, D.F., Mallows, C.L.: Scale mixtures of normal distributions. 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