sp.mantel.mc: Mantel-Hubert spatial general cross product statistic
In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models

Description Usage Arguments Value Author(s) References See Also Examples

A permutation test for the spatial general cross product statistic with Moran (C(i,j) = z(i)*z(j)), Geary (C(i,j) = (z(i) - z(j))^2), and Sokal (C(i,j) = |z(i) - z(j)|) criteria, for z(i) = (x(i) - mean(x))/sd(x). plot.mc.sim is a helper function to plot the outcomes of the permutation test.

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

`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 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".
`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

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.

Roger Bivand Roger.Bivand@nhh.no

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.

moran.mc, joincount.mc, geary.mc

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