gw.weight {GWmodel}

Weight matrix calculation

Description

Calculate a weight vector(matrix) from a distance vector(matrix).

Usage

gw.weight(vdist,bw,kernel,adaptive=FALSE)

Arguments

vdist

a distance matrix or vector

bw

bandwidth used in the weighting function, possibly calculated by bw.gwr;fixed (distance) or adaptive bandwidth(number of nearest neighbours)

kernel

function chosen as follows:

gaussian: wgt = exp(-.5*(vdist/bw)^2);

exponential: wgt = exp(-vdist/bw);

bisquare: wgt = (1-(vdist/bw)^2)^2 if vdist < bw, wgt=0 otherwise;

tricube: wgt = (1-(vdist/bw)^3)^3 if vdist < bw, wgt=0 otherwise;

boxcar: wgt=1 if dist < bw, wgt=0 otherwise

adaptive

if TRUE calculate an adaptive kernel where the bandwidth (bw) corresponds to the number of nearest neighbours (i.e. adaptive distance); default is FALSE, where a fixed kernel is found (bandwidth is a fixed distance)

Value

Returns a numeric weight matrix or vector; matrix with its rows corresponding to the observations and its columns corresponds to the GW model calibration points.

Note

The gaussian and exponential kernel functions are continuous and valued in the interval (0,1]; while bisquare, tricube and boxcar kernel functions are discontinuous and valued in the interval [0,1]. Notably, the upper limit of the bandwidth is exactly the number of observations when the adaptive kernel is used. In this function, the adaptive bandwidth will be specified as the number of observations even though a larger number is assigned. The function will be the same as a global application function (i.e. all weights are 1) when the adaptive bandwidth is equal to or larger than the number of observations when using the boxcar kernel function.

Author(s)

Binbin Lu [e-mail]