sp.mantel.mc: Mantel-Hubert spatial general cross product statistic

In spdep: Spatial Dependence: Weighting Schemes, Statistics

Mantel-Hubert spatial general cross product statistic

Description

A permutation test for the spatial general cross product statistic with Moran (C_{ij} = z_i z_j), Geary (C_{ij} = (z_i - z_j)^2), and Sokal (C_{ij} = |z_i - z_j|) criteria, for z_i = (x_i - \bar{x}) / \sigma_{x}. plot.mc.sim is a helper function to plot the outcomes of the permutation test.

Usage

sp.mantel.mc(var, listw, nsim, type = "moran", zero.policy = attr(listw, "zero.policy"),
 alternative = "greater", spChk=NULL, return_boot=FALSE)
## S3 method for class 'mc.sim'
plot(x, xlim, xlab, main, sub, ..., ptype="density")

Arguments

var	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
type	"moran", "geary" or "sokal" criteria for similarity
zero.policy	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
alternative	a character string specifying the alternative hypothesis, must be one of "greater" (default), "two.sided", or "less".
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
x	the object to be plotted
xlim	the range of the x axis
xlab	a title for the x axis
main	an overall title for the plot
sub	a sub title for the plot
ptype	either "density" or "hist"
...	further arguments passed through

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.
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.
p.value	the pseudo p-value of the test.
res	nsim simulated values of statistic, final value is observed statistic
estimate	the mean and variance of the simulated distribution.

Author(s)

Roger Bivand [e-mail]

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 22-24, Haining, R. 1990 Spatial data analysis in the social and environmental sciences, Cambridge: Cambridge University Press, p. 230–1. The function has been checked against general matrix code posted to the r-help list by Ben Bolker on 1 May 2001; another mantel() function is in the vegan package.

See Also

moran.mc, joincount.mc, geary.mc

Examples

data(oldcol)
sim1 <- sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb),
 nsim=99, type="geary", alternative="two.sided")
sim1
plot(sim1)
sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99,
 type="sokal", alternative="two.sided")
sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99,
 type="moran")

spdep documentation built on Sept. 13, 2024, 5:07 p.m.