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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 P-IRLS estimation with GCV/UBRE smoothness estimation</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 gam.fit {mgcv}"><tr><td>gam.fit {mgcv}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>GAM P-IRLS estimation with GCV/UBRE smoothness estimation</h2> <h3>Description</h3> <p> This is an internal function of package <code>mgcv</code>. It is a modification of the function <code>glm.fit</code>, designed to be called from <code>gam</code> when perfomance iteration is selected (not the default). The major modification is that rather than solving a weighted least squares problem at each IRLS step, a weighted, penalized least squares problem is solved at each IRLS step with smoothing parameters associated with each penalty chosen by GCV or UBRE, using routine <code><a href="magic.html">magic</a></code>. For further information on usage see code for <code>gam</code>. Some regularization of the IRLS weights is also permitted as a way of addressing identifiability related problems (see <code><a href="gam.control.html">gam.control</a></code>). Negative binomial parameter estimation is supported. </p> <p>The basic idea of estimating smoothing parameters at each step of the P-IRLS is due to Gu (1992), and is termed ‘performance iteration’ or 'performance oriented iteration'. </p> <h3>Usage</h3> <pre> gam.fit(G, start = NULL, etastart = NULL, mustart = NULL, family = gaussian(), control = gam.control(),gamma=1, fixedSteps=(control$maxit+1),...) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>G</code></td> <td> <p>An object of the type returned by <code><a href="gam.html">gam</a></code> when <code>fit=FALSE</code>.</p> </td></tr> <tr valign="top"><td><code>start</code></td> <td> <p>Initial values for the model coefficients.</p> </td></tr> <tr valign="top"><td><code>etastart</code></td> <td> <p>Initial values for the linear predictor.</p> </td></tr> <tr valign="top"><td><code>mustart</code></td> <td> <p>Initial values for the expected response.</p> </td></tr> <tr valign="top"><td><code>family</code></td> <td> <p>The family object, specifying the distribution and link to use.</p> </td></tr> <tr valign="top"><td><code>control</code></td> <td> <p>Control option list as returned by <code><a href="gam.control.html">gam.control</a></code>.</p> </td></tr> <tr valign="top"><td><code>gamma</code></td> <td> <p>Parameter which can be increased to up the cost of each effective degree of freedom in the GCV or AIC/UBRE objective.</p> </td></tr> <tr valign="top"><td><code>fixedSteps</code></td> <td> <p>How many steps to take: useful when only using this routine to get rough starting values for other methods.</p> </td></tr> <tr valign="top"><td><code>...</code></td> <td> <p>Other arguments: ignored.</p> </td></tr> </table> <h3>Value</h3> <p>A list of fit information.</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>Gu (1992) Cross-validating non-Gaussian data. J. Comput. Graph. Statist. 1:169-179 </p> <p>Gu and Wahba (1991) Minimizing GCV/GML scores with multiple smoothing parameters via the Newton method. SIAM J. Sci. Statist. Comput. 12:383-398 </p> <p>Wood, S.N. (2000) Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties. J.R.Statist.Soc.B 62(2):413-428 </p> <p>Wood, S.N. (2004) Stable and efficient multiple smoothing parameter estimation for generalized additive models. J. Amer. Statist. Ass. 99:637-686 </p> <h3>See Also</h3> <p><code><a href="gam.fit3.html">gam.fit3</a></code>, <code><a href="gam.html">gam</a></code>, <code><a href="magic.html">magic</a></code></p> <hr /><div style="text-align: center;">[Package <em>mgcv</em> version 1.8-28 <a href="00Index.html">Index</a>]</div> </body></html>