EVOLUTION-MANAGER
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: GAM scaled t family for heavy tailed data</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for scat {mgcv}"><tr><td>scat {mgcv}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>GAM scaled t family for heavy tailed data</h2> <h3>Description</h3> <p>Family for use with <code><a href="gam.html">gam</a></code> or <code><a href="bam.html">bam</a></code>, implementing regression for the heavy tailed response variables, y, using a scaled t model. The idea is that <i>(y - mu)/sig ~ t_nu</i> where <i>mu</i> is determined by a linear predictor, while <i>sig</i> and <i>nu</i> are parameters to be estimated alongside the smoothing parameters. </p> <h3>Usage</h3> <pre> scat(theta = NULL, link = "identity",min.df=3) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>theta</code></td> <td> <p>the parameters to be estimated <i>nu = b + exp(theta_1) </i> (where ‘b’ is <code>min.df</code>) and <i>sig = exp(theta_2)</i>. If supplied and both positive, then taken to be fixed values of <i>nu</i> and <i>sig</i>. If any negative, then absolute values taken as starting values. </p> </td></tr> <tr valign="top"><td><code>link</code></td> <td> <p>The link function: one of <code>"identity"</code>, <code>"log"</code> or <code>"inverse"</code>.</p> </td></tr> <tr valign="top"><td><code>min.df</code></td> <td> <p>minimum degrees of freedom. Should not be set to 2 or less as this implies infinite response variance.</p> </td></tr> </table> <h3>Details</h3> <p>Useful in place of Gaussian, when data are heavy tailed. <code>min.df</code> can be modified, but lower values can occasionally lead to convergence problems in smoothing parameter estimation. In any case <code>min.df</code> should be >2, since only then does a t random variable have finite variance. </p> <h3>Value</h3> <p>An object of class <code>extended.family</code>. </p> <h3>Author(s)</h3> <p> Natalya Pya (nat.pya@gmail.com) </p> <h3>References</h3> <p>Wood, S.N., N. Pya and B. Saefken (2016), Smoothing parameter and model selection for general smooth models. Journal of the American Statistical Association 111, 1548-1575 <a href="http://dx.doi.org/10.1080/01621459.2016.1180986">http://dx.doi.org/10.1080/01621459.2016.1180986</a> </p> <h3>Examples</h3> <pre> library(mgcv) ## Simulate some t data... set.seed(3);n<-400 dat <- gamSim(1,n=n) dat$y <- dat$f + rt(n,df=4)*2 b <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),family=scat(link="identity"),data=dat) b plot(b,pages=1) </pre> <hr /><div style="text-align: center;">[Package <em>mgcv</em> version 1.8-28 <a href="00Index.html">Index</a>]</div> </body></html>