bw.gwda: Bandwidth selection for GW Discriminant Analysis
In GWmodel: Geographically-Weighted Models

bw.gwda

R Documentation

Bandwidth selection for GW Discriminant Analysis

Description

A function for automatic bandwidth selection for GW Discriminant Analysis using a cross-validation approach only

Usage

bw.gwda(formula, data, COV.gw = T, prior.gw = T, mean.gw = T,
                 prior = NULL, wqda = F, kernel = "bisquare", adaptive
                 = FALSE, p = 2, theta = 0, longlat = F,dMat)

Arguments

`formula`	Model formula of a formula object
`data`	a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp, or a sf object defined in package sf
`COV.gw`	if true, localised variance-covariance matrix is used for GW discriminant analysis; otherwise, global variance-covariance matrix is used
`mean.gw`	if true, localised mean is used for GW discriminant analysis; otherwise, global mean is used
`prior.gw`	if true, localised prior probability is used for GW discriminant analysis; otherwise, fixed prior probability is used
`prior`	a vector of given prior probability
`wqda`	if TRUE, a weighted quadratic discriminant analysis will be applied; otherwise a weighted linear discriminant analysis 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 (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

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