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% Copyright 2001-4 by Roger S. Bivand
\encoding{latin1}
\name{moran.mc}
\alias{moran.mc}
\title{Permutation test for Moran's I statistic}
\description{
A permutation test for Moran's I statistic calculated by using nsim random permutations of x for the given spatial weighting scheme, to establish the rank of the observed statistic in relation to the nsim simulated values.
}
\usage{
moran.mc(x, listw, nsim, zero.policy=NULL, alternative="greater",
na.action=na.fail, spChk=NULL, return_boot=FALSE, adjust.n=TRUE)
}
\arguments{
\item{x}{a numeric vector the same length as the neighbours list in listw}
\item{listw}{a \code{listw} object created for example by \code{nb2listw}}
\item{nsim}{number of permutations}
\item{zero.policy}{default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA}
\item{alternative}{a character string specifying the alternative hypothesis, must be one of "greater" (default), or "less".}
\item{na.action}{a function (default \code{na.fail}), can also be \code{na.omit} or \code{na.exclude} - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to \code{nb2listw} may be subsetted. \code{na.pass} is not permitted because it is meaningless in a permutation test.}
\item{spChk}{should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use \code{get.spChkOption()}}
\item{return_boot}{return an object of class \code{boot} from the equivalent permutation bootstrap rather than an object of class \code{htest}}
\item{adjust.n}{default TRUE, if FALSE the number of observations is not adjusted for no-neighbour observations, if TRUE, the number of observations is adjusted}
}
\value{
A list with class \code{htest} and \code{mc.sim} containing the following components:
\item{statistic}{the value of the observed Moran's I.}
\item{parameter}{the rank of the observed Moran's I.}
\item{p.value}{the pseudo p-value of the test.}
\item{alternative}{a character string describing the alternative hypothesis.}
\item{method}{a character string giving the method used.}
\item{data.name}{a character string giving the name(s) of the data, and the number of simulations.}
\item{res}{nsim simulated values of statistic, final value is observed statistic}
}
\references{Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.}
\author{Roger Bivand \email{Roger.Bivand@nhh.no}}
\seealso{\code{\link{moran}}, \code{\link{moran.test}}}
\examples{
data(oldcol)
colw <- nb2listw(COL.nb, style="W")
nsim <- 99
set.seed(1234)
sim1 <- moran.mc(COL.OLD$CRIME, listw=colw, nsim=nsim)
sim1
mean(sim1$res[1:nsim])
var(sim1$res[1:nsim])
summary(sim1$res[1:nsim])
colold.lags <- nblag(COL.nb, 3)
set.seed(1234)
sim2 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
style="W"), nsim=nsim)
summary(sim2$res[1:nsim])
sim3 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
style="W"), nsim=nsim)
summary(sim3$res[1:nsim])
}
\keyword{spatial}
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