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

Calculate Moran's I for spatial variables out of the eigenfunction-based spatial filtering framework. The function also tests each Moran's I with a permutation or parametric test. The calculation of Moran's I and the test of significance are carried out by the function.

1 2 | ```
moran.I.uni(x, mat.W, scaled = FALSE,normalize=FALSE, na.rm = FALSE, test.type="permutation",nperm=999,alternative = "greater")
moran.I.multi(eigenvector.mat,link,weight,scaled=FALSE,normalize=FALSE,na.rm = FALSE,test.type="permutation",nperm=999,plot.res=TRUE)
``` |

`x` |
A numeric vector. |

`mat.W` |
A matrix of weights. |

`eigenvector.mat` |
Matrix. A set of orthogonal spatial variables, created by the function |

`link` |
A 2-column matrix describing the link edges. It has 2 columns (from, to) and as many rows as there are edges. The object names in the From-To list are the order numbers of the objects, not their names if the names differ from the order numbers. |

`weight` |
A vector providing weights associated to the edges. If no weights are given, the function consider all edges to have the same weights. |

`scaled` |
Logical ( |

`normalize` |
Logical ( |

`na.rm` |
Logical ( |

`alternative` |
A character string specifying the alternative hypothesis that is tested against the null hypothesis of no spatial autocorrelation; must be of one "two.sided", "less", or "greater", or any unambiguous abbrevation of these. |

`test.type` |
A character string specifying the type of test to be carried out. Either "permutation", or "parametric", or any unambiguous abbrevation of these. Default is "permutation" |

`nperm` |
Numeric. a number specifying the number of permutation to be carried out. This argument is inactive when performing a parametric test. |

`plot.res` |
Logical ( |

`moran.I.uni`

is a modification of `Moran.I`

(the code was heavily borrowed from library ape). In `Moran.I`

the normalization is carried out by default, whereas in `moran.I.uni`

the choice is given to the user.

Other type of orthogonal spatial variables (MEM, PCNM) created through the Moran's eigenvector maps framework (result of `scores.listw`

or `pcnm`

) can also be tested with those functions.

Function `moran.I.basic`

is simple function to compute Moran's I. It is used by both `moran.I.uni`

and `moran.I.multi`

.

` observed ` |
The computed Moran's I |

` expected ` |
Numeric. The expected Moran's I under the null hypothesis. |

` sd ` |
Numeric. The standard deviation of the Moran's I under the null hypothesis. This value is calculated only during parametric tests. |

`p.value` |
The P-value of the null hypothesis's test against the alternative hypothesis specified in |

` res.mat ` |
A 2-column matrix. The first column gives the observed Moran's I value, the second column gives the associated p-value. |

F. Guillaume Blanchet

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
### Construct AEM eigenfunctions
nb<-cell2nb(5,5,"queen")
xy <- cbind(1:25,expand.grid(1:5,1:5))
bin.mat <- build.binary(nb,xy)
aem1 <- aem(build.binary=bin.mat)
### Calculate and test Moran's I for each AEM eigenfunction
moran.I.multi(aem1$vectors, bin.mat[[2]])
#---------------------------
### Example using spacemakeR
### This section is temporarily in comments because spacemakeR fails to compile on R-forge.
#---------------------------
#require(spacemakeR)
### Construct Moran's eigenvector maps
#nb<-cell2nb(5,5,"queen")
#sc.queen<-scores.listw(nb2listw(nb,style="B"))
### Calculate and test Moran's I for each MEM eigenfunction
#moran.I.multi(sc.queen$vector,listw2sn(nb2listw(nb))[,1:2])
``` |

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