ade4 (version 1.2-2)

gearymoran: Moran's I and Geary'c randomization tests for spatial and phylogenetic autocorrelation

Description

This function performs Moran's I test using phylogenetic and spatial link matrix (binary or general). It uses neighbouring weights so Moran's I and Geary's c randomization tests are equivalent.

Usage

gearymoran(bilis, X, nrepet = 999)

Arguments

bilis

: a n by n link matrix where n is the row number of X

X

: a data frame with continuous variables

nrepet

: number of random vectors for the randomization test

Value

• Returns an object of class krandtest (randomization tests).

Details

bilis is a squared symmetric matrix which terms are all positive or null.

bilis is firstly transformed in frequency matrix A by dividing it by the total sum of data matrix : $$a_{ij} = \frac{bilis_{ij}}{\sum_{i=1}^{n}\sum_{j=1}^{n}bilis_{ij}}$$. The neighbouring weights is defined by the matrix $D = diag(d_1,d_2, \ldots)$ where $d_i = \sum_{j=1}^{n}bilis_{ij}$. For each vector x of the data frame X, the test is based on the Moran statistic $x^{t}Ax$ where x is D-centred.

References

Cliff, A. D. and Ord, J. K. (1973) Spatial autocorrelation, Pion, London.

Thioulouse, J., Chessel, D. and Champely, S. (1995) Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1--14.

See Also

moran.test and geary.test for classical versions of Moran'I test and Geary'c one

Examples

# a spatial example
data(mafragh)
tab0 <- (as.data.frame(scalewt(mafragh$mil)))
bilis0 <- neig2mat(mafragh$neig)
gm0 <- gearymoran(bilis0, tab0, 999)
gm0
plot(gm0, nclass = 20)

# a phylogenetic example
data(mjrochet)
mjr.phy <- newick2phylog(mjrochet$tre)
mjr.tab <- log(mjrochet$tab)
gearymoran(mjr.phy$Amat, mjr.tab)
gearymoran(mjr.phy$Wmat, mjr.tab)
par(mfrow = c(1,2))
table.value(mjr.phy$Wmat, csi = 0.25, clabel.r = 0)
table.value(mjr.phy$Amat, csi = 0.35, clabel.r = 0)
par(mfrow = c(1,1))