R: Mantel-Hubert spatial general cross product statistic

sp.mantel.mc {spdep} | R Documentation

## Mantel-Hubert spatial general cross product statistic

### Description

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.

### Usage

    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")

### 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 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

### 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 Roger.Bivand@nhh.no

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

[Package spdep version 1.2-2 Index]