cov.from.dist {rwc}

Create covariance matrix from a distance matrix

Description

This computes a covariance matrix from a squared-distance matrix using the centering method of Gower (1996). When the squared-distance matrix is a resistance distance matrix, or a variogram matrix from a spatial model, the resulting covariance matrix is the spatial covariance matrix corresponding to a random walk model for connectivity as in Hanks and Hooten (2013).

Usage

cov.from.dist(R)

Arguments

R

A negative semi-definite matrix of squared differences.

Value

A positive semi-definite covariance matrix, for which the variogram (or resistance distance) is equal to the input R matrix.

Author(s)

Ephraim M. Hanks

References

Hanks and Hooten 2013. Circuit theory and model-based inference for landscape connectivity. Journal of the American Statistical Association. 108(501), 22-33.

Gower 1996. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53(3), 325-338.

Examples

## create a Wishart covariance matrix with independent structure
Z=matrix(rnorm(10*20),ncol=20,nrow=10)
W=Z%*%t(Z)

## convert to resistance distance matrix
D=dist.from.cov(W)

## convert back to covariance matrix
C=cov.from.dist(D)

## compare C and W
max(abs(C-W))