DDistMat function

Double-Power Distance Weights Matrix

This function calculates the double-power distance matrix, for a given distance cutoff and a positive exponent.

DDistMat(distMat, distCutOff = NULL, powr = 2, mevn = FALSE)

Arguments

• distMat: distance matrix
• distCutOff: distance cutoff. Default = the maximal value from the distance matrix.
• powr: power (positive exponent), default 2
• 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 $w_{ij} = (1-(\frac{d_{ij}}{D})^p)^p$, if $0 <= d_{ij} < D$ and $w_{ij} = 0$, if $d_{ij} > D$ or $i = j$. D is the cut-off distance point (maximum radius of influence), $d_{ij}$ is the distance between spatial units i and j, and p is the power value (e.g. p = 2, 3, 4,...).

Examples

data(gN3dist) ##distance in meters
W1    <- DDistMat(distMat = gN3dist,
                  distCutOff = 300000,
                  powr = 3) ##distance cutoff in meters
dist2 <- gN3dist/1000 ##in km
W2    <- DDistMat(distMat = dist2, 300, 3)  ##distance cutoff in kilometers

Author(s)

Rozeta Simonovska