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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: The basis of the space of un-penalized functions for a TPRS</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 null.space.dimension {mgcv}"><tr><td>null.space.dimension {mgcv}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>The basis of the space of un-penalized functions for a TPRS</h2> <h3>Description</h3> <p> The thin plate spline penalties give zero penalty to some functions. The space of these functions is spanned by a set of polynomial terms. <code>null.space.dimension</code> finds the dimension of this space, <i>M</i>, given the number of covariates that the smoother is a function of, <i>d</i>, and the order of the smoothing penalty, <i>m</i>. If <i>m</i> does not satisfy <i>2m>d</i> then the smallest possible dimension for the null space is found given <i>d</i> and the requirement that the smooth should be visually smooth. </p> <h3>Usage</h3> <pre> null.space.dimension(d,m) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>d</code></td> <td> <p> is a positive integer - the number of variables of which the t.p.s. is a function. </p> </td></tr> <tr valign="top"><td><code>m</code></td> <td> <p> a non-negative integer giving the order of the penalty functional, or signalling that the default order should be used.</p> </td></tr> </table> <h3>Details</h3> <p> Thin plate splines are only visually smooth if the order of the wiggliness penalty, <i>m</i>, satisfies <i>2m > d+1</i>. If <i>2m<d+1</i> then this routine finds the smallest <i>m</i> giving visual smoothness for the given <i>d</i>, otherwise the supplied <i>m</i> is used. The null space dimension is given by: </p> <p><i>M=(m+d-1)!/(d!(m-1)!</i> </p> <p>which is the value returned. </p> <h3>Value</h3> <p>An integer (array), the null space dimension <i>M</i>. </p> <h3>Author(s)</h3> <p> Simon N. Wood <a href="mailto:simon.wood@r-project.org">simon.wood@r-project.org</a></p> <h3>References</h3> <p>Wood, S.N. (2003) Thin plate regression splines. J.R.Statist.Soc.B 65(1):95-114 </p> <p><a href="http://www.maths.bris.ac.uk/~sw15190/">http://www.maths.bris.ac.uk/~sw15190/</a> </p> <h3>See Also</h3> <p><code><a href="smooth.construct.tp.smooth.spec.html">tprs</a></code></p> <h3>Examples</h3> <pre> require(mgcv) null.space.dimension(2,0) </pre> <hr /><div style="text-align: center;">[Package <em>mgcv</em> version 1.8-28 <a href="00Index.html">Index</a>]</div> </body></html>