Wartenberg's coefficient is a measure of correlation developed by epidemiologist Daniel Wartenberg.
[1] This coefficient is a multivariate extension of spatial autocorrelation that aims to account for spatial dependence of data while studying their covariance.
[2] A modified version of this statistic is available in the R package adespatial.
spatial sites Moran's I is a measure of the spatial autocorrelation of the data.
By standardizing the observations
by subtracting the mean and dividing by the variance as well as normalising the spatial weight matrix such that
we can write Moran's I as Wartenberg generalized this by letting
For larger values of
are the Moran indices for each of the variables and the off-diagonals give the corresponding Wartenberg correlation coefficients.
is an example of a Mantel statistic and so its significance can be evaluated using the Mantel test.
[4] Lee[5] points out some problems with this coefficient namely: He suggests an alternative coefficient which has two factors of
in the numerator and is symmetric for any weight matrix.