ade4 (version 1.7-19)

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, alter=c("greater", "less", "two-sided"))

Value

Returns an object of class krandtest (randomization tests).

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

alter

a character string specifying the alternative hypothesis, must be one of "greater" (default), "less" or "two-sided"

Author

Sébastien Ollier
Daniel Chessel

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's test and Geary's one

Examples

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

if (FALSE) {
# 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)

if(adegraphicsLoaded()) {
  g1 <- table.value(mjr.phy$Wmat, ppoints.cex = 0.35, nclass = 5,
    axis.text = list(cex = 0), plot = FALSE)
  g2 <- table.value(mjr.phy$Amat, ppoints.cex = 0.35, nclass = 5,
    axis.text = list(cex = 0), plot = FALSE)
  G <- cbindADEg(g1, g2, plot = TRUE)
  
} else {
  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))
}
}