GWmodel (version 2.1-3)

gwr.predict: GWR used as a spatial predictor

Description

This function implements basic GWR as a spatial predictor. The GWR prediction function is able to do leave-out-one predictions (when the observation locations are used for prediction) and predictions at a set-aside data set (when unobserved locations are used for prediction).

Usage

gwr.predict(formula, data, predictdata, bw, kernel="bisquare",adaptive=FALSE, p=2,
           theta=0, longlat=F,dMat1, dMat2)
# S3 method for gwrm.pred
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

predictdata

a Spatial*DataFrame object to provide prediction locations, 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)

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

dMat1

a pre-specified distance matrix between data points and prediction locations; if not given, it will be calculated by the given parameters

dMat2

a pre-specified sysmetric distance matrix between data points; if not given, it will be calculated by the given parameters

x

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

...

arguments passed through (unused)

Value

A list of class “gwrm.pred”:

GW.arguments

a list of geographically weighted arguments

SDF

a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package "sp") with GWR coefficients, predictions and prediction variances in its "data" slot.

this.call

the function call used.

References

Harris P, Fotheringham AS, Crespo R, Charlton M (2010) The use of geographically weighted regression for spatial prediction: an evaluation of models using simulated data sets. Mathematical Geosciences 42:657-680

Harris P, Juggins S (2011) Estimating freshwater critical load exceedance data for Great Britain using space-varying relationship models. Mathematical Geosciences 43: 265-292

Harris P, Brunsdon C, Fotheringham AS (2011) Links, comparisons and extensions of the geographically weighted regression model when used as a spatial predictor. Stochastic Environmental Research and Risk Assessment 25:123-138

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

# NOT RUN {
data(LondonHP)
gwr.pred<-gwr.predict(PURCHASE~FLOORSZ, data=londonhp, bw=2000,kernel = "gaussian")
gwr.pred
#########Global OLS regression results and comparison with gstat functions
if(require("gstat"))
{
  mlr.g <- gstat(id = "xx1", formula = PURCHASE~FLOORSZ,data=londonhp)
  mlr.g1 <- predict(mlr.g, newdata = londonhp, BLUE = TRUE)
  mlr.g1
}
############
ols.pred<-gwr.predict(PURCHASE~FLOORSZ, data=londonhp, bw=100000000000000000000000)
ols.pred$SDF
# }