moran.mc.RdA 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.
moran.mc(x, listw, nsim, zero.policy=attr(listw, "zero.policy"),
alternative="greater", na.action=na.fail, spChk=NULL, return_boot=FALSE,
adjust.n=TRUE)a numeric vector the same length as the neighbours list in listw
a listw object created for example by nb2listw
number of permutations
default attr(listw, "zero.policy") as set when listw was created, if attribute not set, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
a character string specifying the alternative hypothesis, must be one of "greater" (default), "two.sided", or "less".
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.
should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()
return an object of class boot from the equivalent permutation bootstrap rather than an object of class htest
default TRUE, if FALSE the number of observations is not adjusted for no-neighbour observations, if TRUE, the number of observations is adjusted
A list with class htest and mc.sim containing the following components:
the value of the observed Moran's I.
the rank of the observed Moran's I.
the pseudo p-value of the test.
a character string describing the alternative hypothesis.
a character string giving the method used.
a character string giving the name(s) of the data, and the number of simulations.
nsim simulated values of statistic, final value is observed statistic
Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.
data(oldcol)
colw <- nb2listw(COL.nb, style="W")
nsim <- 99
set.seed(1234)
sim1 <- moran.mc(COL.OLD$CRIME, listw=colw, nsim=nsim)
sim1
#>
#> Monte-Carlo simulation of Moran I
#>
#> data: COL.OLD$CRIME
#> weights: colw
#> number of simulations + 1: 100
#>
#> statistic = 0.51095, observed rank = 100, p-value = 0.01
#> alternative hypothesis: greater
#>
mean(sim1$res[1:nsim])
#> [1] -0.003196117
var(sim1$res[1:nsim])
#> [1] 0.008543554
summary(sim1$res[1:nsim])
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.180085 -0.073721 -0.009528 -0.003196 0.063865 0.206779
colold.lags <- nblag(COL.nb, 3)
set.seed(1234)
sim2 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
style="W"), nsim=nsim)
summary(sim2$res[1:nsim])
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.15905 -0.07503 -0.01535 -0.02060 0.03305 0.13023
sim3 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
style="W"), nsim=nsim)
summary(sim3$res[1:nsim])
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.192986 -0.055468 -0.024154 -0.026327 0.004769 0.129996
crime <- COL.OLD$CRIME
is.na(crime) <- sample(1:length(crime), 10)
try(moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99,
na.action=na.fail))
#> Error in na.fail.default(x) : missing values in object
moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
na.action=na.omit)
#>
#> Monte-Carlo simulation of Moran I
#>
#> data: crime
#> weights: nb2listw(COL.nb, style = "W")
#> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48
#> number of simulations + 1: 100
#>
#> statistic = 0.42342, observed rank = 100, p-value = 0.01
#> alternative hypothesis: greater
#>
moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
return_boot=TRUE, na.action=na.omit)
#> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48
#>
#> DATA PERMUTATION
#>
#>
#> Call:
#> boot(data = x, statistic = moran_boot, R = nsim, sim = "permutation",
#> listw = listw, n = n, S0 = S0, zero.policy = zero.policy,
#> parallel = parallel, ncpus = ncpus, cl = cl)
#>
#>
#> Bootstrap Statistics :
#> original bias std. error
#> t1* 0.4234221 -0.4429891 0.1293935
moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
na.action=na.exclude)
#>
#> Monte-Carlo simulation of Moran I
#>
#> data: crime
#> weights: nb2listw(COL.nb, style = "W")
#> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48
#> number of simulations + 1: 100
#>
#> statistic = 0.42342, observed rank = 100, p-value = 0.01
#> alternative hypothesis: greater
#>
moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, zero.policy=TRUE,
return_boot=TRUE, na.action=na.exclude)
#> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48
#>
#> DATA PERMUTATION
#>
#>
#> Call:
#> boot(data = x, statistic = moran_boot, R = nsim, sim = "permutation",
#> listw = listw, n = n, S0 = S0, zero.policy = zero.policy,
#> parallel = parallel, ncpus = ncpus, cl = cl)
#>
#>
#> Bootstrap Statistics :
#> original bias std. error
#> t1* 0.4234221 -0.4384413 0.1243937
try(moran.mc(crime, nb2listw(COL.nb, style="W"), nsim=99, na.action=na.pass))
#> Error in moran.mc(crime, nb2listw(COL.nb, style = "W"), nsim = 99, na.action = na.pass) :
#> na.pass not permitted