gwr.lcr.cv.contrib {GWmodel}

Cross-validation data at each observation location for the GWR-LCR model

Description

This function finds the individual cross-validation score at each observation location, for a GWR-LCR model, for a specified bandwidth. These data can be mapped to detect unusually high or low cross-validations scores.

Usage

gwr.lcr.cv.contrib(bw,X,Y,locs,kernel="bisquare",
                    lambda=0,lambda.adjust=FALSE,cn.thresh=NA,
                    adaptive=FALSE, p=2, theta=0, longlat=F,dMat)

Arguments

bw

bandwidth used in the weighting function;fixed (distance) or adaptive bandwidth(number of nearest neighbours)

X

a numeric matrix of the independent data with an extra column of “ones” for the 1st column

Y

a column vector of the dependent data

locs

a two-column numeric array of observation coordinates

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

lambda

option for a globally-defined (constant) ridge parameter. Default is lambda=0, which gives a basic GWR fit

lambda.adjust

a locally-varying ridge parameter. Default FALSE, refers to: (i) a basic GWR without a local ridge adjustment (i.e. lambda=0, everywhere); or (ii) a penalised GWR with a global ridge adjustment (i.e. lambda is user-specified as some constant, other than 0 everywhere); if TRUE, use cn.tresh to set the maximum condition number. Here for locations with a condition number (for its local design matrix) above this user-specified threshold, a local ridge parameter is found

cn.thresh

maximum value for condition number, commonly set between 20 and 30

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)

p

the power of the Minkowski distance, default is 2, i.e. the Euclidean distance

theta

an angle in radians to rotate the coordinate system, default is 0

longlat

if TRUE, great circle distances will be calculated

dMat

a pre-specified distance matrix, it can be calculated by the function gw.dist

Value

CV

a data vector consisting of squared residuals, whose sum is the cross-validation score for the specified bandwidth.

Author(s)

Binbin Lu [e-mail]