bw.gwpca {GWmodel}

Bandwidth selection for Geographically Weighted Principal Components Analysis (GWPCA)

Description

A function for automatic bandwidth selection to calibrate a basic or robust GWPCA via a cross-validation approach only

Usage

bw.gwpca(data,vars,k=2, robust=FALSE,kernel="bisquare",adaptive=FALSE,p=2, 
         theta=0, longlat=F,dMat)

Arguments

data

a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp

vars

a vector of variable names to be evaluated

k

the number of retained components, and it must be less than the number of variables

robust

if TRUE, robust GWPCA will be applied; otherwise basic GWPCA will be applied

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 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

Returns the adaptive or fixed distance bandwidth

Note

For a discontinuous kernel function, a bandwidth can be specified either as a fixed (constant) distance or as a fixed (constant) number of local data (i.e. an adaptive distance). For a continuous kernel function, a bandwidth can be specified either as a fixed distance or as a 'fixed quantity that reflects local sample size' (i.e. still an 'adaptive' distance but the actual local sample size will be the sample size as functions are continuous). In practise a fixed bandwidth suits fairly regular sample configurations whilst an adaptive bandwidth suits highly irregular sample configurations. Adaptive bandwidths ensure sufficient (and constant) local information for each local calibration. This note is applicable to all GW models

Author(s)

Binbin Lu [e-mail]

References

Harris P, Clarke A, Juggins S, Brunsdon C, Charlton M (2015) Enhancements to a geographically weighted principal components analysis in the context of an application to an environmental data set. Geographical Analysis 47: 146-172