gwr.lcr: GWR with a locally-compensated ridge term

In GWmodel: Geographically-Weighted Models

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 class 'gwrlcr'
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, 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)

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.

Author(s)

Binbin Lu [e-mail]

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)

GWmodel documentation built on Sept. 11, 2024, 9:09 p.m.