GWmodel (version 2.4-1)

gwr.lcr: 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)
# S3 method for gwrlcr
print(x, ...)

Value

A list of class “rgwr”:

SDF

a SpatialPointsDataFrame (may be gridded), or SpatialPolygonsDataFrame object (see package “sp”), or sf object (see package “sf”) 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.

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

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

x

an object of class “gwrlcr”, returned by the function gwr.lcr

...

arguments passed through (unused)

Author

Binbin Lu

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)$d
  cn <- Xsvd[1] / Xsvd[p]
  cn
}
#
X <- cbind(1,Dub.voter@data[,3:10])
head(X)
CN.global <- BKW_cn(X)
CN.global
if (FALSE) {
# gwr.lcr function with a global bandwidth to check that the global CN is found
gwr.lcr1 <- gwr.lcr(GenEl2004~DiffAdd+LARent+SC1+Unempl+LowEduc+Age18_24
+Age25_44+Age45_64, data=Dub.voter, bw=10000000000)
summary(gwr.lcr1$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")
}