GWmodel (version 2.1-3)

gwr.basic: Basic GWR model

Description

This function implements basic GWR

Usage

gwr.basic(formula, data, regression.points, bw, kernel="bisquare",
adaptive=FALSE, p=2, theta=0, longlat=F,dMat,F123.test=F,cv=F, W.vect=NULL)
# S3 method for gwrm
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

regression.points

a Spatial*DataFrame object, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp; Note that no diagnostic information will returned if it is assigned

bw

bandwidth used in the weighting function, possibly calculated by bw.gwr;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

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

If TRUE, conduct three seperate F-tests according to Leung et al. (2000).

cv

if TRUE, cross-validation data will be calculated and returned in the output Spatial*DataFrame

W.vect

default NULL, if given it will be used to weight the distance weighting matrix

x

an object of class “gwrm”, returned by the function gwr.basic

...

arguments passed through (unused)

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.

timings

starting and ending time.

this.call

the function call used.

Ftest.res

results of Leung's F tests when F123.test is TRUE.

References

Brunsdon, C, Fotheringham, S, Charlton, M (1996), Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity. Geographical Analysis 28(4):281-298

Charlton, M, Fotheringham, S, and Brunsdon, C (2007), GWR3.0, http://gwr.nuim.ie/.

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

Leung, Y, Mei, CL, and Zhang, WX (2000), Statistical tests for spatial nonstationarity based on the geographically weighted regression model. Environment and Planning A, 32, 9-32.

Lu, B, Charlton, M, Harris, P, Fotheringham, AS (2014) Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data. International Journal of Geographical Information Science 28(4): 660-681

Examples

# NOT RUN {
data(LondonHP)
DM<-gw.dist(dp.locat=coordinates(londonhp))
##Compare the time consumed with and without a specified distance matrix
# }
# NOT RUN {
system.time(gwr.res<-gwr.basic(PURCHASE~FLOORSZ, data=londonhp, bw=1000,
            kernel = "gaussian"))
system.time(DM<-gw.dist(dp.locat=coordinates(londonhp)))
system.time(gwr.res<-gwr.basic(PURCHASE~FLOORSZ, data=londonhp, bw=1000,
            kernel = "gaussian", dMat=DM))

## specify an optimum bandwidth by cross-validation appraoch
bw1<-bw.gwr(PURCHASE~FLOORSZ, data=londonhp, kernel = "gaussian",dMat=DM)
gwr.res1<-gwr.basic(PURCHASE~FLOORSZ, data=londonhp, bw=bw1,kernel = "gaussian", 
                   dMat=DM)
gwr.res1 
# }
# NOT RUN {
data(LondonBorough)

nsa = list("SpatialPolygonsRescale", layout.north.arrow(), offset = c(561900,200900), 
scale = 500, col=1)
# }
# NOT RUN {
if(require("RColorBrewer"))
{
  mypalette<-brewer.pal(6,"Spectral")
  x11()
  spplot(gwr.res1$SDF, "FLOORSZ", key.space = "right", cex=1.5, cuts=10,
  ylim=c(155840.8,200933.9), xlim=c(503568.2,561957.5),
  main="GWR estimated coefficients for FLOORSZ with a fixed bandwidth", 
  col.regions=mypalette, sp.layout=list(nsa, londonborough))}
# }
# NOT RUN {
bw2<-bw.gwr(PURCHASE~FLOORSZ,approach="aic",adaptive=TRUE, data=londonhp, 
            kernel = "gaussian", dMat=DM)
gwr.res2<-gwr.basic(PURCHASE~FLOORSZ, data=londonhp, bw=bw2,adaptive=TRUE,
                    kernel = "gaussian", dMat=DM)
gwr.res2
if(require("RColorBrewer"))
{
  x11()
  spplot(gwr.res2$SDF, "FLOORSZ", key.space = "right", cex=1.5, cuts=10,
  ylim=c(155840.8,200933.9), xlim=c(503568.2,561957.5),
  main="GWR estimated coefficients for FLOORSZ with an adaptive bandwidth", 
  col.regions=mypalette, sp.layout=list(nsa,londonborough))}
# }