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

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"))

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"

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.

Value

Returns an object of class krandtest (randomization tests).

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.

Author

Sébastien Ollier sebastien.ollier@u-psud.fr
Daniel Chessel

Examples

# a spatial example
data(mafragh)
tab0 <- (as.data.frame(scalewt(mafragh$env)))
bilis0 <- neig2mat(nb2neig(mafragh$nb))
gm0 <- gearymoran(bilis0, tab0, 999)
gm0
#> class: krandtest lightkrandtest 
#> Monte-Carlo tests
#> Call: as.krandtest(sim = matrix(res$result, ncol = nvar, byrow = TRUE), 
#>     obs = res$obs, alter = alter, names = test.names)
#> 
#> Number of tests:   11 
#> 
#> Adjustment method for multiple comparisons:   none 
#> Permutation number:   999 
#>            Test        Obs   Std.Obs   Alter Pvalue
#> 1          Clay 0.42436873  7.122114 greater  0.001
#> 2          Silt 0.33796853  5.937642 greater  0.001
#> 3          Sand 0.09947991  1.709492 greater  0.054
#> 4           K2O 0.27277951  4.770128 greater  0.001
#> 5          Mg++ 0.18577104  3.306797 greater  0.002
#> 6      Na+/100g 0.26673592  4.716987 greater  0.001
#> 7            K+ 0.66106701 11.247309 greater  0.001
#> 8  Conductivity 0.29969555  5.281175 greater  0.001
#> 9     Retention 0.20099816  3.623479 greater  0.002
#> 10        Na+/l 0.24300034  4.366741 greater  0.001
#> 11    Elevation 0.59526831 10.136647 greater  0.001
#> 
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))
}
}