bw.gwr.lcr: Bandwidth selection for locally compensated ridge GWR...

In GWmodel: Geographically-Weighted Models

Bandwidth selection for locally compensated ridge GWR (GWR-LCR)

Description

A function for automatic bandwidth selection for gwr.lcr via a cross-validation approach only

Usage

bw.gwr.lcr(formula, data, kernel="bisquare",
        lambda=0,lambda.adjust=FALSE,cn.thresh=NA,
        adaptive=FALSE, p=2, theta=0, longlat=F,dMat)

Arguments

formula	Regression model formula of a formula object
data	a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp
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
p	the power of the Minkowski distance, default is 2, i.e. the Euclidean distance
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. 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 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)
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

Gollini I, Lu B, Charlton M, Brunsdon C, Harris P (2015) GWmodel: an R Package for exploring Spatial Heterogeneity using Geographically Weighted Models. Journal of Statistical Software 63(17): 1-50

GWmodel documentation built on July 9, 2023, 5:52 p.m.