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% File nlme/man/Variogram.default.Rd
% Part of the nlme package for R
% Distributed under GPL 2 or later: see nlme/LICENCE
% $Id: Variogram.default.Rd,v 1.8.2.1 2003/04/17 22:28:45 bates Exp $
\name{Variogram.default}
\title{Calculate Semi-variogram}
\usage{
\method{Variogram}{default}(object, distance, \dots)
}
\alias{Variogram.default}
\arguments{
\item{object}{a numeric vector with the values to be used for
calculating the semi-variogram, usually a residual vector from a
fitted model.}
\item{distance}{a numeric vector with the pairwise distances
corresponding to the elements of \code{object}. The order of the
elements in \code{distance} must correspond to the pairs
\code{(1,2), (1,3), \dots, (n-1,n)}, with \code{n} representing the
length of \code{object}, and must have length \code{n(n-1)/2}.}
\item{\dots}{some methods for this generic require additional
arguments. None are used in this method.}
}
\description{
This method function calculates the semi-variogram for an arbitrary
vector \code{object}, according to the distances in \code{distance}.
For each pair of elements \eqn{x,y} in \code{object}, the
corresponding semi-variogram is \eqn{(x-y)^2/2}. The semi-variogram is
useful for identifying and modeling spatial correlation structures in
observations with constant expectation and constant variance.
}
\value{
a data frame with columns \code{variog} and \code{dist} representing,
respectively, the semi-variogram values and the corresponding
distances. The returned value inherits from class \code{Variogram}.
}
\references{
Cressie, N.A.C. (1993), "Statistics for Spatial Data", J. Wiley & Sons.
}
\author{Jose Pinheiro \email{Jose.Pinheiro@pharma.novartis.com} and Douglas Bates \email{bates@stat.wisc.edu}}
\seealso{
\code{\link{Variogram}},
\code{\link{Variogram.gls}},
\code{\link{Variogram.lme}},
\code{\link{plot.Variogram}}}
\examples{
\dontrun{
fm1 <- lm(follicles ~ sin(2 * pi * Time) + cos(2 * pi * Time), Ovary,
subset = Mare == 1)
Variogram(resid(fm1), dist(1:29))[1:10,]
}
}
\keyword{models}
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