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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: Exponential Correlation Structure</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 corExp {nlme}"><tr><td>corExp {nlme}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Exponential Correlation Structure</h2> <h3>Description</h3> <p>This function is a constructor for the <code>"corExp"</code> class, representing an exponential spatial correlation structure. Letting <i>d</i> denote the range and <i>n</i> denote the nugget effect, the correlation between two observations a distance <i>r</i> apart is <i>exp(-r/d)</i> when no nugget effect is present and <i>(1-n)*exp(-r/d)</i> when a nugget effect is assumed. Objects created using this constructor must later be initialized using the appropriate <code>Initialize</code> method. </p> <h3>Usage</h3> <pre> corExp(value, form, nugget, metric, fixed) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>value</code></td> <td> <p>an optional vector with the parameter values in constrained form. If <code>nugget</code> is <code>FALSE</code>, <code>value</code> can have only one element, corresponding to the "range" of the exponential correlation structure, which must be greater than zero. If <code>nugget</code> is <code>TRUE</code>, meaning that a nugget effect is present, <code>value</code> can contain one or two elements, the first being the "range" and the second the "nugget effect" (one minus the correlation between two observations taken arbitrarily close together); the first must be greater than zero and the second must be between zero and one. Defaults to <code>numeric(0)</code>, which results in a range of 90% of the minimum distance and a nugget effect of 0.1 being assigned to the parameters when <code>object</code> is initialized.</p> </td></tr> <tr valign="top"><td><code>form</code></td> <td> <p>a one sided formula of the form <code>~ S1+...+Sp</code>, or <code>~ S1+...+Sp | g</code>, specifying spatial covariates <code>S1</code> through <code>Sp</code> and, optionally, a grouping factor <code>g</code>. When a grouping factor is present in <code>form</code>, the correlation structure is assumed to apply only to observations within the same grouping level; observations with different grouping levels are assumed to be uncorrelated. Defaults to <code>~ 1</code>, which corresponds to using the order of the observations in the data as a covariate, and no groups.</p> </td></tr> <tr valign="top"><td><code>nugget</code></td> <td> <p>an optional logical value indicating whether a nugget effect is present. Defaults to <code>FALSE</code>.</p> </td></tr> <tr valign="top"><td><code>metric</code></td> <td> <p>an optional character string specifying the distance metric to be used. The currently available options are <code>"euclidean"</code> for the root sum-of-squares of distances; <code>"maximum"</code> for the maximum difference; and <code>"manhattan"</code> for the sum of the absolute differences. Partial matching of arguments is used, so only the first three characters need to be provided. Defaults to <code>"euclidean"</code>.</p> </td></tr> <tr valign="top"><td><code>fixed</code></td> <td> <p>an optional logical value indicating whether the coefficients should be allowed to vary in the optimization, or kept fixed at their initial value. Defaults to <code>FALSE</code>, in which case the coefficients are allowed to vary.</p> </td></tr> </table> <h3>Value</h3> <p>an object of class <code>"corExp"</code>, also inheriting from class <code>"corSpatial"</code>, representing an exponential spatial correlation structure. </p> <h3>Author(s)</h3> <p>José Pinheiro and Douglas Bates <a href="mailto:bates@stat.wisc.edu">bates@stat.wisc.edu</a></p> <h3>References</h3> <p>Cressie, N.A.C. (1993), "Statistics for Spatial Data", J. Wiley & Sons. </p> <p>Venables, W.N. and Ripley, B.D. (2002) "Modern Applied Statistics with S", 4th Edition, Springer-Verlag. </p> <p>Littel, Milliken, Stroup, and Wolfinger (1996) "SAS Systems for Mixed Models", SAS Institute. </p> <p>Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer, esp. p. 238. </p> <h3>See Also</h3> <p><code><a href="corClasses.html">corClasses</a></code>, <code><a href="Initialize.corStruct.html">Initialize.corStruct</a></code>, <code><a href="summary.corStruct.html">summary.corStruct</a></code>, <code><a href="../../stats/html/dist.html">dist</a></code> </p> <h3>Examples</h3> <pre> sp1 <- corExp(form = ~ x + y + z) # Pinheiro and Bates, p. 238 spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4) cs1Exp <- corExp(1, form = ~ x + y) cs1Exp <- Initialize(cs1Exp, spatDat) corMatrix(cs1Exp) cs2Exp <- corExp(1, form = ~ x + y, metric = "man") cs2Exp <- Initialize(cs2Exp, spatDat) corMatrix(cs2Exp) cs3Exp <- corExp(c(1, 0.2), form = ~ x + y, nugget = TRUE) cs3Exp <- Initialize(cs3Exp, spatDat) corMatrix(cs3Exp) # example lme(..., corExp ...) # Pinheiro and Bates, pp. 222-247 # p. 222 options(contrasts = c("contr.treatment", "contr.poly")) fm1BW.lme <- lme(weight ~ Time * Diet, BodyWeight, random = ~ Time) # p. 223 fm2BW.lme <- update(fm1BW.lme, weights = varPower()) # p. 246 fm3BW.lme <- update(fm2BW.lme, correlation = corExp(form = ~ Time)) # p. 247 fm4BW.lme <- update(fm3BW.lme, correlation = corExp(form = ~ Time, nugget = TRUE)) anova(fm3BW.lme, fm4BW.lme) </pre> <hr /><div style="text-align: center;">[Package <em>nlme</em> version 3.1-139 <a href="00Index.html">Index</a>]</div> </body></html>