GWmodel (version 2.4-1)

gwr.robust: 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)

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”), or sf object (see package “sf”) 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.

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.

Author

Binbin Lu

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

if (FALSE) {
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")
}
}