spdep (version 0.4-9)

moran.mc: 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. The examples show how boot(sim="permutation") can replicate this function (thanks to Virgilio G�mez Rubio and the DCluster package).

Usage

moran.mc(x, listw, nsim, zero.policy=FALSE, alternative="greater",
 na.action=na.fail, spChk=NULL)

Arguments

x

a numeric vector the same length as the neighbours list in listw

listw

a listw object created for example by nb2listw

nsim

number of permutations

zero.policy

if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA

alternative

a character string specifying the alternative hypothesis, must be one of "greater" (default), or "less".

na.action

a function (default na.fail), can also be na.omit or 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 ma

spChk

should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()

Value

• A list with class htest and mc.sim containing the following components:
• statistic
  the value of the observed Moran's I.
• parameter
  the rank of the observed Moran's I.
• p.value
  the pseudo p-value of the test.
• alternative
  a character string describing the alternative hypothesis.
• method
  a character string giving the method used.
• data.name
  a character string giving the name(s) of the data, and the number of simulations.
• res
  nsim simulated values of statistic, final value is observed statistic

encoding

latin1

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.

See Also

moran, 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])
MoranI.boot <- function(var, i, ...) {
var <- var[i]
return(moran(x=var, ...)$I)
}
set.seed(1234)
library(boot)
boot1 <- boot(COL.OLD$CRIME, statistic=MoranI.boot, R=nsim,
 sim="permutation", listw=colw, n=nrow(COL.OLD), S0=Szero(colw))
boot1
plot(boot1)
mean(boot1$t)
var(boot1$t)
summary(boot1$t)
colold.lags <- nblag(COL.nb, 3)
set.seed(1234)
sim2 <- moran.mc(COL.OLD$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])