gwr.bootstrap: Bootstrap GWR

In GWmodel: Geographically-Weighted Models

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 class 'gwrbsm'
print(x, ...)

Arguments

formula	Regression model formula of a formula object
data	a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp
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)

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”) integrated with fit.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.

Note

This function implements the bootstrap methods introduced in Harris et al. (2017). It provides a global test statistic (the modified one given in Harris et al. 2017) and a complementary localised version that can be mapped. The bootstrap methods test for coefficient variability found from GWR under model assumptions for each of four null hypotheses: i) multiple linear regression model (MLR); ii) simultaneous autoregressive error model (ERR); iii) moving average error model (SMA) and iv) simultaneous autoregressive lag model (LAG).

Author(s)

Binbin Lu [e-mail]

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

## Not run: 
#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")))

## End(Not run)

GWmodel documentation built on July 9, 2023, 5:52 p.m.