# 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

1 2 3 4 |

### Arguments

`var` |
a numeric vector the same length as the neighbours list in listw |

`listw` |
a |

`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 |

`return_boot` |
return an object of class |

`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

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