1% Copyright 2001-4 by Roger S. Bivand
2\encoding{latin1}
3\name{moran.mc}
4\alias{moran.mc}
5\title{Permutation test for Moran's I statistic}
6\description{
7 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.
8}
9\usage{
10moran.mc(x, listw, nsim, zero.policy=NULL, alternative="greater",
11 na.action=na.fail, spChk=NULL, return_boot=FALSE, adjust.n=TRUE)
12}
13\arguments{
14  \item{x}{a numeric vector the same length as the neighbours list in listw}
15  \item{listw}{a \code{listw} object created for example by \code{nb2listw}}
16  \item{nsim}{number of permutations}
17  \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}
18  \item{alternative}{a character string specifying the alternative hypothesis, must be one of "greater" (default), or "less".}
19  \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.}
20  \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()}}
21  \item{return_boot}{return an object of class \code{boot} from the equivalent permutation bootstrap rather than an object of class \code{htest}}
22  \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}
23}
24
25\value{
26A list with class \code{htest} and \code{mc.sim} containing the following components:
27  \item{statistic}{the value of the observed Moran's I.}
28  \item{parameter}{the rank of the observed Moran's I.}
29  \item{p.value}{the pseudo p-value of the test.}
30  \item{alternative}{a character string describing the alternative hypothesis.}
31  \item{method}{a character string giving the method used.}
32  \item{data.name}{a character string giving the name(s) of the data, and the number of simulations.}
33  \item{res}{nsim simulated values of statistic, final value is observed statistic}
34}
35\references{Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.}
36\author{Roger Bivand \email{Roger.Bivand@nhh.no}}
37
38\seealso{\code{\link{moran}}, \code{\link{moran.test}}}
39
40\examples{
41data(oldcol)
42colw <- nb2listw(COL.nb, style="W")
43nsim <- 99
44set.seed(1234)
45sim1 <- moran.mc(COL.OLD$CRIME, listw=colw, nsim=nsim)
46sim1
47mean(sim1$res[1:nsim])
48var(sim1$res[1:nsim])
49summary(sim1$res[1:nsim])
50colold.lags <- nblag(COL.nb, 3)
51set.seed(1234)
52sim2 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
53 style="W"), nsim=nsim)
54summary(sim2$res[1:nsim])
55sim3 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
56 style="W"), nsim=nsim)
57summary(sim3$res[1:nsim])
58}
59\keyword{spatial}
60