moranbi.mc {bispdep}

Permutation test for bivariate Moran's Ixy statistic

Description

A permutation test for bivariate Moran's Ixy statistic calculated by using nsim random permutations of x and y for the given spatial weighting scheme, to establish the rank of the observed statistic in relation to the nsim simulated values.

Usage

moranbi.mc(varX, varY, listw, nsim, zero.policy=NULL, alternative="greater",
           na.action=na.fail, spChk=NULL, return_boot=FALSE, adjust.n=TRUE, parallel="no",
           ncpus = getOption("boot.ncpus", 1L), cl = NULL)

Arguments

varX

a numeric vector of the variable x the same length as the neighbours list in listw

varY

a numeric vector of the variable y the same length as the neighbours list in listw

listw

a listw object created for example by nb2listw

nsim

number of permutations

zero.policy

default NULL, use global option value; 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), "two.sided", 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 may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted. na.pass is not permitted because it is meaningless in a permutation test.

spChk

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

return_boot

return an object of class boot from the equivalent permutation bootstrap rather than an object of class htest

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

parallel

The type of parallel operation to be used (if any). If missing, the default is "no". for more details see boot

ncpus

integer: number of processes to be used in parallel operation: number of available CPUs. By default it is set to 1 with getOption("boot.ncpus", 1L)

cl

An optional parallel or snow cluster for use if parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of the boot call (by default is NULL).

Value

A list with class htest and mc.sim containing the following components:

statistic

the value of the observed bivariate Moran's I.

parameter

the rank of the observed bivariate 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

References

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

See Also

moran.bi, moranbi.test

Examples

library(spdep)
data(oldcol)
colw <- nb2listw(COL.nb, style="W")
nsim <- 999
set.seed(123)
sim1 <- moranbi.mc(COL.OLD$CRIME, COL.OLD$INC, listw=colw, nsim=nsim, zero.policy=TRUE)
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 <- moranbi.mc(COL.OLD$CRIME, COL.OLD$INC, nb2listw(colold.lags[[2]],style="W"),
                   nsim=nsim, zero.policy=TRUE)
summary(sim2$res[1:nsim])
sim3 <- moranbi.mc(COL.OLD$CRIME, COL.OLD$INC, nb2listw(colold.lags[[3]],style="W"),
                   nsim=nsim, zero.policy=TRUE)
summary(sim3$res[1:nsim])
sim4 <- moranbi.mc(COL.OLD$CRIME, COL.OLD$INC, colw, nsim=nsim, zero.policy=TRUE,
                   return_boot=TRUE,parallel="multicore")
sim4