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Last data update: 2014.03.03

R: GWR with a locally-compensated ridge term

gwr.lcr

R Documentation

GWR with a locally-compensated ridge term

Description

To address possible local collinearity problems in basic GWR, GWR-LCR finds local ridge parameters at affected locations (set by a user-specified threshold for the design matrix condition number).

Usage

gwr.lcr(formula, data, regression.points, bw, kernel="bisquare",
                    lambda=0,lambda.adjust=FALSE,cn.thresh=NA,
                    adaptive=FALSE, p=2, theta=0, longlat=F,cv=T,dMat)

Arguments

`formula`	Regression model formula of a formula object
`data`	a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp
`regression.points`	a Spatial*DataFrame object, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp, or a two-column numeric array
`bw`	bandwidth used in the weighting function, possibly calculated by `bw.gwr.lcr`; fixed (distance) or adaptive bandwidth(number of nearest neighbours)
`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
`p`	the power of the Minkowski distance, default is 2, i.e. the Euclidean distance
`lambda`	option for a globally-defined (constant) ridge parameter. Default is lambda=0, which gives a basic GWR fit
`lambda.adjust`	a locally-varying ridge parameter. Default FALSE, refers to: (i) a basic GWR without a local ridge adjustment (i.e. lambda=0, everywhere); or (ii) a penalised GWR with a global ridge adjustment (i.e. lambda is user-specified as some constant, other than 0 everywhere); if TRUE, use cn.tresh to set the maximum condition number. Here for locations with a condition number (for its local design matrix) above this user-specified threshold, a local ridge parameter is found
`cn.thresh`	maximum value for condition number, commonly set between 20 and 30
`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)
`theta`	an angle in radians to rotate the coordinate system, default is 0
`longlat`	if TRUE, great circle distances will be calculated
`cv`	if TRUE, 'cross-validation data will be calculated and returned in the output Spatial*DataFrame
`dMat`	a pre-specified distance matrix, it can be calculated by the function `gw.dist`

Value

A list of class “rgwr”:

`SDF`	a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package "sp") with coordinates of regression.points in its "data" slot.
`GW.arguments`	parameters used for the LCR-GWR calibration
`GW.diagnostic`	diagnostic information is given when data points are also used as regression locations
`timings`	timing information for running this function
`this.call`	the function call used.

Author(s)

Binbin Lu binbinlu@whu.edu.cn

References

Wheeler D (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A 39:2464-2481

Brunsdon C, Charlton M, Harris P (2012) Living with collinearity in Local Regression Models. GISRUK 2012, Lancaster, UK

Brunsdon C, Charlton M, Harris P (2012) Living with collinearity in Local Regression Models. Spatial Accuracy 2012, Brazil

Gollini I, Lu B, Charlton M, Brunsdon C, Harris P (2015) GWmodel: an R Package for exploring Spatial Heterogeneity using Geographically Weighted Models. Journal of Statistical Software 63(17): 1-50

Examples

data(DubVoter)
require(RColorBrewer)

# Function to find the global condition number (CN)
BKW_cn <- function (X) {
  p <- dim(X)[2]
  Xscale <- sweep(X, 2, sqrt(colSums(X^2)), "/")
  Xsvd <- svd(Xscale)$d
  cn <- Xsvd[1] / Xsvd[p]
  cn
}
#
X <- cbind(1,Dub.voter@data[,3:10])
head(X)
CN.global <- BKW_cn(X)
CN.global
## Not run: 
# gwr.lcr function with a global bandwidth to check that the global CN is found
gwr.lcr1 <- gwr.lcr(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
+Age25_44+Age45_64, data=Dub.voter, bw=10000000000)
summary(gwr.lcr1$SDF$Local_CN)

# Find and map the local CNs from a basic GWR fit using the lcr-gwr function 
#(note this is NOT the locally-compensated ridge GWR fit as would need to set 
#lambda.adjust=TRUE and cn.thresh=30, say)

bw.lcr2 <- bw.gwr.lcr(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
+Age25_44+Age45_64, data=Dub.voter, kernel="bisquare", adaptive=TRUE)
gwr.lcr2 <- gwr.lcr(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
+Age25_44+Age45_64, data=Dub.voter, bw=bw.lcr2, kernel="bisquare", adaptive=TRUE)
if(require("RColorBrewer"))
  spplot(gwr.lcr2$SDF,"Local_CN",col.regions=brewer.pal(9,"YlOrRd"),cuts=8,
  main="Local CN")

## End(Not run)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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> library(GWmodel)
Loading required package: maptools
Loading required package: sp
Checking rgeos availability: TRUE
Loading required package: robustbase
Welcome to GWmodel version 1.2-5.
 Note: The default kernel for all the functions have been set as bisquare from this release
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GWmodel/gwr.lcr.rd_%03d_medium.png", width=480, height=480)
> ### Name: gwr.lcr
> ### Title: GWR with a locally-compensated ridge term
> ### Aliases: gwr.lcr ridge.lm
> ### Keywords: ridge, GWR
> 
> ### ** Examples
> 
> data(DubVoter)
> require(RColorBrewer)
Loading required package: RColorBrewer
> 
> # Function to find the global condition number (CN)
> BKW_cn <- function (X) {
+   p <- dim(X)[2]
+   Xscale <- sweep(X, 2, sqrt(colSums(X^2)), "/")
+   Xsvd <- svd(Xscale)$d
+   cn <- Xsvd[1] / Xsvd[p]
+   cn
+ }
> #
> X <- cbind(1,Dub.voter@data[,3:10])
> head(X)
  1        Y  DiffAdd    LARent       SC1    Unempl  LowEduc Age18_24 Age25_44
0 1 235244.0 22.08633 16.208791  8.561151  8.009709 0.600000 24.17266 39.56835
1 1 234933.8 23.59987 22.388060  7.898996 12.126156 0.585586 21.88411 45.48398
2 1 234162.9 33.51579 75.438596 10.610526  8.940201 0.522648 28.04210 49.68421
3 1 234506.9 13.95918 37.298637  5.469388 15.185602 0.698758 14.66667 39.29252
4 1 234737.3 13.88697 13.615870  6.960717 13.021807 0.579581 11.95727 38.04273
5 1 236758.4  6.49846  1.668255  6.043714  2.882353 0.193632 11.88206 33.87120
> CN.global <- BKW_cn(X)
> CN.global
[1] 131.3154
> ## Not run: 
> ##D # gwr.lcr function with a global bandwidth to check that the global CN is found
> ##D gwr.lcr1 <- gwr.lcr(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
> ##D +Age25_44+Age45_64, data=Dub.voter, bw=10000000000)
> ##D summary(gwr.lcr1$SDF$Local_CN)
> ##D 
> ##D # Find and map the local CNs from a basic GWR fit using the lcr-gwr function 
> ##D #(note this is NOT the locally-compensated ridge GWR fit as would need to set 
> ##D #lambda.adjust=TRUE and cn.thresh=30, say)
> ##D 
> ##D bw.lcr2 <- bw.gwr.lcr(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
> ##D +Age25_44+Age45_64, data=Dub.voter, kernel="bisquare", adaptive=TRUE)
> ##D gwr.lcr2 <- gwr.lcr(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
> ##D +Age25_44+Age45_64, data=Dub.voter, bw=bw.lcr2, kernel="bisquare", adaptive=TRUE)
> ##D if(require("RColorBrewer"))
> ##D   spplot(gwr.lcr2$SDF,"Local_CN",col.regions=brewer.pal(9,"YlOrRd"),cuts=8,
> ##D   main="Local CN")
> ## End(Not run)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>