GWmodel (version 2.4-1)

gwr.montecarlo: Monte Carlo (randomisation) test for significance of GWR parameter variability

Description

This function implements a Monte Carlo (randomisation) test to test for significant (spatial) variability of a GWR model's parameters or coefficients.

Usage

gwr.montecarlo(formula, data = list(),nsims=99, kernel="bisquare",adaptive=F, bw,
                         p=2, theta=0, longlat=F,dMat)

Value

pmat

A vector containing p-values for all the GWR parameters

Arguments

formula

Regression 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

nsims

the number of randomisations

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)

bw

bandwidth used in the weighting function, possibly calculated by bw.gwr

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

Brunsdon C, Fotheringham AS, Charlton ME (1998) Geographically weighted regression - modelling spatial non-stationarity. Journal of the Royal Statistical Society, Series D-The Statistician 47(3):431-443

Fotheringham S, Brunsdon, C, and Charlton, M (2002), Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, Chichester: Wiley.

Charlton, M, Fotheringham, S, and Brunsdon, C (2007), GWR3.0.

Examples

if (FALSE) {
data(LondonHP)
DM<-gw.dist(dp.locat=coordinates(londonhp))
bw<-bw.gwr(PURCHASE~FLOORSZ,data=londonhp,dMat=DM, kernel="gaussian")
#See any difference in the next two commands and why?
res.mont1<-gwr.montecarlo(PURCHASE~PROF+FLOORSZ, data = londonhp,dMat=DM,
nsim=99, kernel="gaussian", adaptive=FALSE, bw=3000)
res.mont2<-gwr.montecarlo(PURCHASE~PROF+FLOORSZ, data = londonhp,dMat=DM,
nsim=99, kernel="gaussian", adaptive=FALSE, bw=300000000000)
}