bw.gwda {GWmodel}

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 for training, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp

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

Author(s)

Binbin Lu [e-mail]