GWmodel (version 2.4-1)

gwr.bootstrap: Bootstrap GWR

Description

This function implements bootstrap methods to test for coefficient variability found from GWR under model assumptions for each of four null hypotheses: MLR, ERR, SMA and LAG models. Global test statistic results are found, as well local observation-specific test results that can be mapped.

Usage

gwr.bootstrap(formula, data, kernel = "bisquare", approach = "AIC",
                 R = 99, k.nearneigh = 4, adaptive = FALSE, p = 2,
                 theta = 0, longlat = FALSE, dMat, verbose = FALSE,
                 parallel.method = FALSE, parallel.arg = NULL)
# S3 method for gwrbsm
print(x, ...)

Value

A list of class “gwrbsm”:

formula

Regression model formula of a formula object

results

modified statistics reported from comparisons between GWR and MLR, ERR, SMA and LAG

SDF

a SpatialPointsDataFrame (may be gridded), or SpatialPolygonsDataFrame object (see package “sp”), or sf object (see package “sf”) integrated with regression.points, GWR coefficient estimates, y value,predicted values, coefficient standard errors and bootstrap p-values in its “data” slot.

timings

starting and ending time.

this.call

the function call used.

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

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

approach

specified by CV for cross-validation approach or by AIC corrected (AICc) approach

R

number of random samples reapted in the bootstrap procedure

k.nearneigh

number of nearest neighbours concerned in calbrating ERR, SMA and LAG models

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

verbose

if TRUE and bandwidth selection is undertaken, the bandwidth searches are reported

x

an object of class “gwrbsm”, returned by the function gwr.bootstrap

parallel.method

FALSE as default, and the calibration will be conducted traditionally via the serial technique, "omp": multi-thread technique with the OpenMP API, "cluster": multi-process technique with the parallel package, "cuda": parallel computing technique with CUDA

parallel.arg

if parallel.method is not FALSE, then set the argument by following: if parallel.method is "omp", parallel.arg refers to the number of threads used, and its default value is the number of cores - 1; if parallel.method is "cluster", parallel.arg refers to the number of R sessions used, and its default value is the number of cores - 1; if parallel.method is "cuda", parallel.arg refers to the number of calibrations included in each group, but note a too large value may cause the overflow of GPU memory.

...

arguments passed through (unused)

Author

Binbin Lu

References

Harris, P., Brunsdon, C., Lu, B., Nakaya, T., & Charlton, M. (2017). Introducing bootstrap methods to investigate coefficient non-stationarity in spatial regression models. Spatial Statistics, 21, 241-261.

Examples

if (FALSE) {
#Example with the Georgia educational attainment data
data(Georgia)
data(GeorgiaCounties)
coords <- cbind(Gedu.df$X, Gedu.df$Y)
Gedu.spdf <- SpatialPointsDataFrame(coords, Gedu.df)
#Make a SpatialPolygonDataFrame
require(RColorBrewer)
gSRDF <- SpatialPolygonsDataFrame(polygons(Gedu.counties), over(Gedu.counties, 
                                  Gedu.spdf),match.ID=T)  
mypalette.1 <- brewer.pal(11,"Spectral")
X11(width=9,height=8)                   
spplot(gSRDF, names(gSRDF)[c(5,7:9)], col.regions=mypalette.1,
cuts=10, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Georgia educational attainment predictor data")))
bsm.res <- gwr.bootstrap(PctBach~PctRural+PctEld+PctFB+PctPov, gSRDF, 
                         R=999, longlat=T)
bsm.res
#local bootstrap tests with respect to: MLR, ERR, SMA and LAG models.
mypalette.local.test <- brewer.pal(10,"Spectral")
X11(width=12,height=16)
spplot(bsm.res$SDF, names(bsm.res$SDF)[14:17], col.regions=mypalette.local.test,
cuts=9, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Local p-values for each coefficient of the MLR model 
                       null hypothesis")))

X11(width=12,height=16)
spplot(bsm.res$SDF, names(bsm.res$SDF)[19:22], col.regions=mypalette.local.test,
cuts=9, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Local p-values for each coefficient of the ERR model 
                       null hypothesis")))
X11(width=12,height=16)
spplot(bsm.res$SDF, names(bsm.res$SDF)[24:27], col.regions=mypalette.local.test,
cuts=9, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Local p-values for each coefficient of the SMA model null
                       hypothesis")))

X11(width=12,height=16)
spplot(bsm.res$SDF, names(bsm.res$SDF)[29:32], col.regions=mypalette.local.test,
cuts=9, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Local p-values for each coefficient of the LAG model null
                       hypothesis")))
################################################################################
#Example with Dublin voter data
data(DubVoter)
X11(width=9,height=8)                   
spplot(Dub.voter, names(Dub.voter)[c(5,7,9,10)], col.regions=mypalette.1,
cuts=10, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Dublin voter turnout predictor data")))
bsm.res1 <- gwr.bootstrap(GenEl2004~LARent+Unempl+Age18_24+Age25_44, Dub.voter
                         , R=999)
bsm.res1

#local bootstrap tests with respect to: MLR, ERR, SMA and LAG models.
X11(width=11,height=8)
spplot(bsm.res1$SDF, names(bsm.res1$SDF)[14:17], col.regions=mypalette.local.test,
cuts=9, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Local p-values for each coefficient of the MLR model null
                        hypothesis")))
X11(width=11,height=8)
spplot(bsm.res1$SDF, names(bsm.res1$SDF)[19:22], col.regions=mypalette.local.test,
cuts=9, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Local p-values for each coefficient of the ERR model null
                        hypothesis")))
X11(width=11,height=8)
spplot(bsm.res1$SDF, names(bsm.res1$SDF)[24:27], col.regions=mypalette.local.test,
cuts=9, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Local p-values for each coefficient of the SMA model 
                            null hypothesis")))
X11(width=11,height=8)
spplot(bsm.res1$SDF, names(bsm.res1$SDF)[29:32], col.regions=mypalette.local.test,
cuts=9, par.settings=list(fontsize=list(text=15)),
main=expression(paste("Local p-values for each coefficient of the LAG model 
                            null hypothesis")))
}