geary.mc: Permutation test for Geary's C statistic

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

Description

A permutation test for Geary's C 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

geary.mc(x, listw, nsim, zero.policy=NULL, alternative="greater",
 spChk=NULL, adjust.n=TRUE, return_boot=FALSE)

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"; this reversal corresponds to that on geary.test described in the section on the output statistic value, based on Cliff and Ord 1973, p. 21 (changed 2011-04-11, thanks to Daniel Garavito).
spChk	should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()
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
return_boot	return an object of class boot from the equivalent permutation bootstrap rather than an object of class htest

Value

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

statistic	the value of the observed Geary's C.
parameter	the rank of the observed Geary's C.
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

geary, geary.test

Examples

data(oldcol)
sim1 <- geary.mc(COL.OLD$CRIME, nb2listw(COL.nb, style="W"),
 nsim=99, alternative="less")
sim1
mean(sim1$res)
var(sim1$res)
summary(sim1$res)
colold.lags <- nblag(COL.nb, 3)
sim2 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
 style="W"), nsim=99)
sim2
summary(sim2$res)
sim3 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
 style="W"), nsim=99)
sim3
summary(sim3$res)

Example output

Loading required package: sp
Loading required package: Matrix

	Monte-Carlo simulation of Geary C

data:  COL.OLD$CRIME 
weights: nb2listw(COL.nb, style = "W") 
number of simulations + 1: 100 

statistic = 0.52987, observed rank = 1, p-value = 0.99
alternative hypothesis: less

[1] 0.9941682
[1] 0.01274658
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.5299  0.9326  1.0070  0.9942  1.0670  1.2527 

	Monte-Carlo simulation of Geary C

data:  COL.OLD$CRIME 
weights: nb2listw(colold.lags[[2]], style = "W") 
number of simulations + 1: 100 

statistic = 0.81129, observed rank = 2, p-value = 0.02
alternative hypothesis: greater

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.7915  0.9351  0.9943  0.9940  1.0563  1.1780 

	Monte-Carlo simulation of Geary C

data:  COL.OLD$CRIME 
weights: nb2listw(colold.lags[[3]], style = "W") 
number of simulations + 1: 100 

statistic = 1.1303, observed rank = 97, p-value = 0.97
alternative hypothesis: greater

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.8464  0.9194  0.9836  0.9842  1.0421  1.2688 

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