GWmodel (version 2.4-1)

gwpca.montecarlo.2: Monte Carlo (randomisation) test for significance of GWPCA eigenvalue variability for the first component only - option 2

Description

This function implements a Monte Carlo (randomisation) test for a basic or robust GW PCA with the bandwidth automatically re-selected via the cross-validation approach. The test evaluates whether the GW eigenvalues vary significantly across space for the first component only.

Usage

gwpca.montecarlo.2(data, vars, k = 2, nsims=99,robust = FALSE, scaling=T, 
                   kernel = "bisquare", adaptive = FALSE,  p = 2, 
                   theta = 0, longlat = F, dMat)

Value

A list of components:

actual

the observed standard deviations (SD) of eigenvalues

sims

a vector of the simulated SDs of eigenvalues

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; k must be less than the number of variables

nsims

the number of simulations for MontCarlo test

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 (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

Author

Binbin Lu

References

Harris P, Brunsdon C, Charlton M (2011) Geographically weighted principal components analysis. International Journal of Geographical Information Science 25:1717-1736

Examples

if (FALSE) {
data(DubVoter)
DM<-gw.dist(dp.locat=coordinates(Dub.voter))
gmc.res.autow<-gwpca.montecarlo.2(data=Dub.voter, vars=c("DiffAdd", "LARent",
"SC1", "Unempl", "LowEduc"), dMat=DM,adaptive=TRUE)
gmc.res.autow
plot.mcsims(gmc.res.autow)
}