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GWmodel (version 2.4-1)

bw.gwpca: 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, scaling=T, kernel="bisquare",adaptive=FALSE,p=2, 
         theta=0, longlat=F,dMat)

Value

Returns the adaptive or fixed distance bandwidth

Arguments

data

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

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

scaling

if TRUE, the data is scaled to have zero mean and unit variance (standardized); otherwise the data is centered but not scaled

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

Author

Binbin Lu binbinlu@whu.edu.cn

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