gwr.robust: Robust GWR model

In GWmodel: Geographically-Weighted Models

Robust GWR model

Description

This function implements two robust GWR models.

Usage

gwr.robust(formula, data, bw,filtered=FALSE, kernel = "bisquare", adaptive = FALSE, p = 2, 
          theta = 0, longlat = F, dMat, F123.test = F, maxiter=20,cut.filter= 3,cut1=2,
          cut2=3,delta=1.0e-5, parallel.method = FALSE, parallel.arg = NULL)  

Arguments

formula	Regression model formula of a formula object
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.gwr;fixed (distance) or adaptive bandwidth(number of nearest neighbours)
filtered	default FALSE, the automatic approach is used, if TRUE the filtered data approach is employed, as that described in Fotheringham et al. (2002 p.73-80)
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
F123.test	default FALSE, otherwise calculate F-test results (Leung et al. 2000)
maxiter	default 20, maximum number of iterations for the automatic approach
cut.filter	If filtered is TRUE, it will be used as the residual cutoff for filtering data; default cutoff is 3
cut1	default 2, first cutoff for the residual weighting function. wr(e)=1 if |e|<=cut1*sigma
cut2	default 3, second cutoff for the residual weighting function. wr(e)=(1-(|e|-2)^2)^2 if cut1*sigma<|e|<cut2*sigma, and wr(e)=0 if |e|>=cut2*sigma; cut 1 and cut2 refer to the automatic approach
delta	default 1.0e-5, tolerance of the iterative algorithm
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.

Value

A list of class “gwrm”:

GW.arguments	a list class object including the model fitting parameters for generating the report file
GW.diagnostic	a list class object including the diagnostic information of the model fitting
lm	an object of class inheriting from “lm”, see lm.
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 t-values in its "data" slot. Notably, E_weigts will be also included in the output SDF which represents the residual weighting when automatic approach is used; When the filtered approach is used, E_weight is a vector consisted of 0 and 1, where 0 means outlier to be excluded from calibration.
timings	starting and ending time.
this.call	the function call used.
Ftest.res	results of Leung's F tests when F123.test is TRUE.

Author(s)

Binbin Lu [e-mail]

References

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

Harris P, Fotheringham AS, Juggins S (2010) Robust geographically weighed regression: a technique for quantifying spatial relationships between freshwater acidification critical loads and catchment attributes. Annals of the Association of American Geographers 100(2): 286-306

Examples

## Not run: 
data(DubVoter)
bw.a <- bw.gwr(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
+Age25_44+Age45_64,
data=Dub.voter,approach="AICc",kernel="bisquare",adaptive=TRUE)
bw.a
gwr.res <- gwr.basic(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
+Age25_44+Age45_64,
data=Dub.voter,bw=bw.a,kernel="bisquare",adaptive=TRUE,F123.test=TRUE)
print(gwr.res)

# Map of the estimated coefficients for LowEduc
names(gwr.res$SDF)
if(require("RColorBrewer"))
{
  mypalette<-brewer.pal(6,"Spectral")
  X11(width=10,height=12)
  spplot(gwr.res$SDF,"LowEduc",key.space = "right",
  col.regions=mypalette,at=c(-8,-6,-4,-2,0,2,4),
  main="Basic GW regression coefficient estimates for LowEduc")
}
# Robust GW regression and map of the estimated coefficients for LowEduc
rgwr.res <- gwr.robust(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
+Age25_44+Age45_64, data=Dub.voter,bw=bw.a,kernel="bisquare",
adaptive=TRUE,F123.test=TRUE)
print(rgwr.res)
if(require("RColorBrewer"))
{
  X11(width=10,height=12)
  spplot(rgwr.res$SDF, "LowEduc", key.space = "right",
  col.regions=mypalette,at=c(-8,-6,-4,-2,0,2,4),
  main="Robust GW regression coefficient estimates for LowEduc")
}

## End(Not run)

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