GWmodel (version 2.4-1)

gwpca.montecarlo.1: Monte Carlo (randomisation) test for significance of GWPCA eigenvalue variability for the first component only - option 1

Description

This function implements a Monte Carlo (randomisation) test for a basic or robust GW PCA with the bandwidth pre-specified and constant. The test evaluates whether the GW eigenvalues vary significantly across space for the first component only.

Usage

gwpca.montecarlo.1(data, bw, vars, k = 2, nsims=99,robust = FALSE, scaling=T, 
                   kernel = "bisquare", adaptive = FALSE,  p = 2, theta = 0, 
                   longlat = F, dMat)
# S3 method for mcsims
plot(x, sname="SD of local eigenvalues from randomisations", ...)

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

bw

bandwidth used in the weighting function, possibly calculated by bw.gwpca;fixed (distance) or adaptive bandwidth(number of nearest neighbours)

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

x

an object of class “mcsims”, returned by the function gwpca.montecarlo.1 or gwpca.montecarlo.2

sname

the label for the observed value on the plot

...

arguments passed through (unused)

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<-gwpca.montecarlo.1(data=Dub.voter, vars=c("DiffAdd", "LARent",
"SC1", "Unempl", "LowEduc"), bw=20,dMat=DM,adaptive=TRUE)
gmc.res
plot(gmc.res)
}