moran.I.multi: Moran's I for symmetric and asymmetric weighting matrix
In AEM: Tools to construct Asymmetric eigenvector maps (AEM) spatial variables

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.

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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 `aem`.
`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 (`TRUE`, `FALSE`) determining if the index should be scaled to allow comparisons between indices (default to `FALSE`).
`normalize`	Logical (`TRUE`, `FALSE`) determining if the matrix of weights should be row-normalized to 1 (default to `FALSE`).
`na.rm`	Logical (`TRUE`, `FALSE`) determining whether missing values should be removed (default to `FALSE`).
`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 (`TRUE`, `FALSE`) determining if the expected and observed values and the results of the test of significance of Moran's I, for each AEM eigenfunction, should be plotted (default to `TRUE`).

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 `alternative`
`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

Moran.I

### 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])