ExpDistMat function

Exponential distance matrix

This function calculates the (negative) exponential distance matrix, with a given cutoff distance and a positive exponent value.

ExpDistMat(distMat, distCutOff = NULL, expn = 0.01, mevn = FALSE)

Arguments

• distMat: distance matrix
• distCutOff: cutoff distance. Default = the maximal value from the distance matrix.
• expn: positive exponent, default = 0.01
• mevn: logical, default FALSE. If TRUE, max-eigenvalue normalization is performed.

Returns

• W: spatial weights matrix (Default, not normalized)

Details

W is an nxn matrix with elements $w_{ij}$, i, j = 1,..n, where $w_{ij}=e^{-\alpha d_{ij}}$, if $0 <= d_{ij} < D$ and $w_{ij}=0$, if $d_{ij} > D$ or $i = j$. D is the distance cutoff point (maximum radius of influence), $d_{ij}$ is the distance between spatial units i and j, and $\alpha$ is the positive exponent (e.g. $\alpha$= 0.01, 0.02,...).

Examples

data(gN3dist) ##distance in meters
W1    <- ExpDistMat(distMat = gN3dist, distCutOff = 100000)
dist2 <- gN3dist/1000 ##in km
W2    <- ExpDistMat(distMat = dist2, distCutOff = 100, expn = 0.02)
W2nor <- ExpDistMat(distMat = dist2, 100000, 0.001, mevn = TRUE)

Author(s)

Rozeta Simonovska