gwpca.montecarlo.1: Monte Carlo (randomisation) test for significance of GWPCA...

In GWmodel: Geographically-Weighted Models

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 class 'mcsims'
plot(x, sname="SD of local eigenvalues from randomisations", ...)

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)

Value

A list of components:

actual	the observed standard deviations (SD) of eigenvalues
sims	a vector of the simulated SDs of eigenvalues

Note

The function “montecarlo.gwpca.1” (in the early versions of GWmodel) has been renamed as “gwpca.montecarlo.1”, while the old name is still kept valid.

Author(s)

Binbin Lu [e-mail]

References

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

Examples

## Not run: 
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)

## End(Not run)

GWmodel documentation built on Sept. 11, 2024, 9:09 p.m.