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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: Calculate Semi-variogram for Residuals from an lme Object</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 Variogram.lme {nlme}"><tr><td>Variogram.lme {nlme}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Calculate Semi-variogram for Residuals from an lme Object</h2> <h3>Description</h3> <p>This method function calculates the semi-variogram for the within-group residuals from an <code>lme</code> fit. The semi-variogram values are calculated for pairs of residuals within the same group. If <code>collapse</code> is different from <code>"none"</code>, the individual semi-variogram values are collapsed using either a robust estimator (<code>robust = TRUE</code>) defined in Cressie (1993), or the average of the values within the same distance interval. The semi-variogram is useful for modeling the error term correlation structure. </p> <h3>Usage</h3> <pre> ## S3 method for class 'lme' Variogram(object, distance, form, resType, data, na.action, maxDist, length.out, collapse, nint, breaks, robust, metric, ...) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>object</code></td> <td> <p>an object inheriting from class <code>"<a href="lme.html">lme</a>"</code>, representing a fitted linear mixed-effects model.</p> </td></tr> <tr valign="top"><td><code>distance</code></td> <td> <p>an optional numeric vector with the distances between residual pairs. If a grouping variable is present, only the distances between residual pairs within the same group should be given. If missing, the distances are calculated based on the values of the arguments <code>form</code>, <code>data</code>, and <code>metric</code>, unless <code>object</code> includes a <code>corSpatial</code> element, in which case the associated covariate (obtained with the <code>getCovariate</code> method) is used.</p> </td></tr> <tr valign="top"><td><code>form</code></td> <td> <p>an optional one-sided formula specifying the covariate(s) to be used for calculating the distances between residual pairs and, optionally, a grouping factor for partitioning the residuals (which must appear to the right of a <code>|</code> operator in <code>form</code>). Default is <code>~1</code>, implying that the observation order within the groups is used to obtain the distances.</p> </td></tr> <tr valign="top"><td><code>resType</code></td> <td> <p>an optional character string specifying the type of residuals to be used. If <code>"response"</code>, the "raw" residuals (observed - fitted) are used; else, if <code>"pearson"</code>, the standardized residuals (raw residuals divided by the corresponding standard errors) are used; else, if <code>"normalized"</code>, the normalized residuals (standardized residuals pre-multiplied by the inverse square-root factor of the estimated error correlation matrix) are used. Partial matching of arguments is used, so only the first character needs to be provided. Defaults to <code>"pearson"</code>.</p> </td></tr> <tr valign="top"><td><code>data</code></td> <td> <p>an optional data frame in which to interpret the variables in <code>form</code>. By default, the same data used to fit <code>object</code> is used.</p> </td></tr> <tr valign="top"><td><code>na.action</code></td> <td> <p>a function that indicates what should happen when the data contain <code>NA</code>s. The default action (<code>na.fail</code>) causes an error message to be printed and the function to terminate, if there are any incomplete observations.</p> </td></tr> <tr valign="top"><td><code>maxDist</code></td> <td> <p>an optional numeric value for the maximum distance used for calculating the semi-variogram between two residuals. By default all residual pairs are included.</p> </td></tr> <tr valign="top"><td><code>length.out</code></td> <td> <p>an optional integer value. When <code>object</code> includes a <code>corSpatial</code> element, its semi-variogram values are calculated and this argument is used as the <code>length.out</code> argument to the corresponding <code>Variogram</code> method. Defaults to <code>50</code>.</p> </td></tr> <tr valign="top"><td><code>collapse</code></td> <td> <p>an optional character string specifying the type of collapsing to be applied to the individual semi-variogram values. If equal to <code>"quantiles"</code>, the semi-variogram values are split according to quantiles of the distance distribution, with equal number of observations per group, with possibly varying distance interval lengths. Else, if <code>"fixed"</code>, the semi-variogram values are divided according to distance intervals of equal lengths, with possibly different number of observations per interval. Else, if <code>"none"</code>, no collapsing is used and the individual semi-variogram values are returned. Defaults to <code>"quantiles"</code>.</p> </td></tr> <tr valign="top"><td><code>nint</code></td> <td> <p>an optional integer with the number of intervals to be used when collapsing the semi-variogram values. Defaults to <code>20</code>.</p> </td></tr> <tr valign="top"><td><code>robust</code></td> <td> <p>an optional logical value specifying if a robust semi-variogram estimator should be used when collapsing the individual values. If <code>TRUE</code> the robust estimator is used. Defaults to <code>FALSE</code>.</p> </td></tr> <tr valign="top"><td><code>breaks</code></td> <td> <p>an optional numeric vector with the breakpoints for the distance intervals to be used in collapsing the semi-variogram values. If not missing, the option specified in <code>collapse</code> is ignored.</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>...</code></td> <td> <p>some methods for this generic require additional arguments. None are used in this method.</p> </td></tr> </table> <h3>Value</h3> <p>a data frame with columns <code>variog</code> and <code>dist</code> representing, respectively, the semi-variogram values and the corresponding distances. If the semi-variogram values are collapsed, an extra column, <code>n.pairs</code>, with the number of residual pairs used in each semi-variogram calculation, is included in the returned data frame. If <code>object</code> includes a <code>corSpatial</code> element, a data frame with its corresponding semi-variogram is included in the returned value, as an attribute <code>"modelVariog"</code>. The returned value inherits from class <code>Variogram</code>. </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> <h3>See Also</h3> <p><code><a href="lme.html">lme</a></code>, <code><a href="Variogram.html">Variogram</a></code>, <code><a href="Variogram.default.html">Variogram.default</a></code>, <code><a href="Variogram.gls.html">Variogram.gls</a></code>, <code><a href="plot.Variogram.html">plot.Variogram</a></code> </p> <h3>Examples</h3> <pre> fm1 <- lme(weight ~ Time * Diet, data=BodyWeight, ~ Time | Rat) Variogram(fm1, form = ~ Time | Rat, nint = 10, robust = TRUE) </pre> <hr /><div style="text-align: center;">[Package <em>nlme</em> version 3.1-139 <a href="00Index.html">Index</a>]</div> </body></html>