A permutation test for Moran's I statistic calculated by using nsim random permutations of x for the given spatial weighting scheme, to establish the rank of the observed statistic in relation to the nsim simulated values.

1 2 |

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

`listw` |
a |

`nsim` |
number of permutations |

`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". |

`na.action` |
a function (default |

`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 |

`adjust.n` |
default TRUE, if FALSE the number of observations is not adjusted for no-neighbour observations, if TRUE, the number of observations is adjusted |

A list with class `htest`

and `mc.sim`

containing the following components:

`statistic` |
the value of the observed Moran's I. |

`parameter` |
the rank of the observed Moran's I. |

`p.value` |
the pseudo p-value of the test. |

`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. |

`res` |
nsim simulated values of statistic, final value is observed statistic |

Roger Bivand Roger.Bivand@nhh.no

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
data(oldcol)
colw <- nb2listw(COL.nb, style="W")
nsim <- 99
set.seed(1234)
sim1 <- moran.mc(COL.OLD$CRIME, listw=colw, nsim=nsim)
sim1
mean(sim1$res[1:nsim])
var(sim1$res[1:nsim])
summary(sim1$res[1:nsim])
colold.lags <- nblag(COL.nb, 3)
set.seed(1234)
sim2 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]],
style="W"), nsim=nsim)
summary(sim2$res[1:nsim])
sim3 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]],
style="W"), nsim=nsim)
summary(sim3$res[1:nsim])
``` |

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