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

 sp.mantel.mc 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.

`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")
```

spdep documentation built on April 18, 2022, 9:06 a.m.