gwr.basic: Basic GWR model

In GWmodel: Geographically-Weighted Models

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,
parallel.method=FALSE,parallel.arg=NULL)
## S3 method for class '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, or a sf object defined in package sf
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
parallel.method	FALSE as default, and the calibration will be conducted traditionally via the serial technique, "omp": multi-thread technique with the OpenMP API, "cluster": multi-process technique with the parallel package, "cuda": parallel computing technique with CUDA
parallel.arg	if parallel.method is not FALSE, then set the argument by following: if parallel.method is "omp", parallel.arg refers to the number of threads used, and its default value is the number of cores - 1; if parallel.method is "cluster", parallel.arg refers to the number of R sessions used, and its default value is the number of cores - 1; if parallel.method is "cuda", parallel.arg refers to the number of calibrations included in each group, but note a too large value may cause the overflow of GPU memory.
...	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”), or sf object (see package “sf”) integrated with regression.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.

Note

Requirements of using CUDA for high-performence computation in GWR functions:

To run GWR-CUDA (i.e. parallel.method is pecified as “cuda”) with gwr.basic , bw.gwr and gwr.model.selection, the following conditions are required:

1. There is at least one NVIDIA GPU supporting CUDA equipped on user's computer.

2. CUDA (>10.2) are installed with the environment variable 'CUDA_HOME' set properly.

3. The package should re-built from source. - For Linux user, 'GWmodelCUDA' will be automatically built if CUDA toolkit could be detected by the complier. - For Windows user, 'GWmodelCUDA.dll' and 'GWmodelCUDA.lib' will be automatically downloaded; however, we would recommend users to build the 'GWmodelCUDA' library manually to avoid some potentially unknown issues, and an 'CMakeLists.txt' file is provided for this procedure.

If any condition above is not satisfied, the GWR-CUDA will not work even though the “parallel.method” is specified as “cuda”.

Author(s)

Binbin Lu [e-mail]

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

OpenMP: https://www.openmp.org/

CUDA: https://developer.nvidia.com/cuda-zone

R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.

Examples

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 
## End(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))}

## End(Not run)
## 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))}

## End(Not run)
## Not run: 
  ############HP-GWR test code
  simulate.data.generator <- function(data.length) {
  x1 <- rnorm(data.length)
  x2 <- rnorm(data.length)
  x3 <- rnorm(data.length)
  lon <- rnorm(data.length, mean = 533200, sd = 10000)
  lat <- rnorm(data.length, mean = 159400, sd = 10000)
  y <- x1 + 5 * x2 + 2.5 * x3 + rnorm(data.length)
  simulate.data <- data.frame(y = y, x1 = x1, x2 = x2, x3 = x3, lon = lon, lat = lat)
  coordinates(simulate.data) <- ~ lon + lat
  names(simulate.data)
  return(simulate.data)
}
simulate.data <- simulate.data.generator(10000)
adaptive = TRUE

## GWR (not parallelized)
bw.CV.s <- bw.gwr(data = simulate.data, formula = y ~ x1 + x2 + x3, approach="CV", 
                  kernel = "gaussian", adaptive = adaptive, parallel.method = FALSE)
model.s <- gwr.model.selection(DeVar = "y", InDeVars = c("x1", "x2", "x3"), data = simulate.data, 
                              bw = bw.CV.s, approach="AIC", kernel = "gaussian", adaptive = T, 
                              parallel.method = FALSE)
system.time(
  betas.s <- gwr.basic(data = simulate.data, formula = y ~ x1 + x2 + x3, bw = bw.CV.s, 
                       kernel = "gaussian", adaptive = TRUE)
)

## GWR-Omp
bw.CV.omp <- bw.gwr(data = simulate.data, formula = y ~ x1 + x2 + x3, approach="CV", 
                    kernel = "gaussian", adaptive = adaptive, parallel.method = "omp")
model.omp <- gwr.model.selection(DeVar = "y", InDeVars = c("x1", "x2", "x3"), data = simulate.data, 
                                bw = bw.CV.omp, approach="AIC", kernel = "gaussian", adaptive = T, 
                                parallel.method = "omp")
system.time(
  betas.omp <- gwr.basic(data = simulate.data, formula = y ~ x1 + x2 + x3, bw = bw.CV.omp, 
                        kernel = "gaussian", adaptive = T, parallel.method = "omp"))

## GWR-CUDA
bw.CV.cuda <- bw.gwr(data = simulate.data, formula = y ~ x1 + x2 + x3, approach="CV", 
                     kernel = "gaussian", adaptive = adaptive, parallel.method = "cuda", 
                     parallel.arg = 6*16)
model.cuda <- gwr.model.selection(DeVar = "y", InDeVars = c("x1", "x2", "x3"), 
                                 data = simulate.data, bw = bw.CV.cuda, approach="AIC", 
                                 kernel = "gaussian", adaptive = T, 
                                 parallel.method = "cuda", parallel.arg = 6*16)
system.time(
  betas.cuda <- gwr.basic(data = simulate.data, formula = y ~ x1 + x2 + x3, bw = bw.CV.cuda, 
                          kernel = "gaussian", adaptive = T, parallel.method = "cuda", 
                          parallel.arg = 6*8))

## End(Not run)

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