These two Monte Carlo tests are used to assess the existence of 'global' and
'local' spatial structures, corresponding respectively to positive and
negative Moran's I .
global.rtest(X, listw, k = 1, nperm = 499)An object of class randtest.
a data matrix, with variables in columns
a list of weights of class listw. Can be obtained easily
using the function chooseCN.
integer: the number of highest \(R^2\) summed to form the test statistics
integer: the number of randomisations to be performed.
Thibaut Jombart t.jombart@imperial.ac.uk
They rely on the decomposition of a data matrix X into global and local components using multiple regression on Moran's Eigenvector Maps (MEMs). They require a data matrix (X) and a list of weights derived from a connection network. X is regressed onto global MEMs (U+) in the global test and on local ones (U-) in the local test. One mean \(R^2\) is obtained for each MEM, the k highest being summed to form the test statistic.
The reference distribution of these statistics are obtained by randomly permuting the rows of X.
These tests were originally part of the adegenet package for R.
Jombart, T., Devillard, S., Dufour, A.-B. and Pontier, D. 2008. Revealing cryptic spatial patterns in genetic variability by a new multivariate method. Heredity, 101, 92--103. doi: 10.1038/hdy.2008.34.