moran.mc: Permutation test for Moran's I statistic

In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models

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

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	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), 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

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

Author(s)

Roger Bivand [e-mail]

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])
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])

Example output

Loading required package: sp
Loading required package: Matrix

	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

[1] -0.01735822
[1] 0.008938155
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-0.238206 -0.083268 -0.007406 -0.017358  0.039717  0.259444 
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-0.18440 -0.06090 -0.01837 -0.01522  0.02860  0.23554 
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-0.16812 -0.06701 -0.02035 -0.01733  0.02200  0.14342 

spdep documentation built on Aug. 19, 2017, 3:01 a.m.