GWmodel (version 2.4-1)

gwss: Geographically weighted summary statistics (GWSS)

Description

This function calculates basic and robust GWSS. This includes geographically weighted means, standard deviations and skew. Robust alternatives include geographically weighted medians, inter-quartile ranges and quantile imbalances. This function also calculates basic geographically weighted covariances together with basic and robust geographically weighted correlations.

Usage

gwss(data, summary.locat,vars,kernel="bisquare",adaptive=FALSE, bw,p=2, 
            theta=0, longlat=F,dMat,quantile=FALSE)
# S3 method for gwss
print(x, ...)

Value

A list of class “lss”:

SDF

a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package “sp”) with local means,local standard deviations,local variance, local skew,local coefficients of variation, local covariances, local correlations (Pearson's), local correlations (Spearman's), local medians, local interquartile ranges, local quantile imbalances and coordinates.

...

other information for reporting

Arguments

data

a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp

summary.locat

a Spatial*DataFrame object for providing summary locations, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp

vars

a vector of variable names to be summarized

bw

bandwidth used in the weighting function

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

quantile

if TRUE, median, interquartile range, quantile imbalance will be calculated

x

an object of class “gwss”, returned by the function gwss

...

arguments passed through (unused)

Author

Binbin Lu

References

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

Brunsdon C, Fotheringham AS, Charlton ME (2002) Geographically weighted summary statistics - a framework for localised exploratory data analysis. Computers, Environment and Urban Systems 26:501-524

Harris P, Clarke A, Juggins S, Brunsdon C, Charlton M (2014) Geographically weighted methods and their use in network re-designs for environmental monitoring. Stochastic Environmental Research and Risk Assessment 28: 1869-1887

Examples

if (FALSE) {
data(EWHP)
data(EWOutline)
head(ewhp)
houses.spdf <- SpatialPointsDataFrame(ewhp[, 1:2], ewhp)
localstats1 <- gwss(houses.spdf, vars = c("PurPrice", "FlrArea"), bw = 50000)
head(data.frame(localstats1$SDF))
localstats1
##A function for mapping data
if(require("RColorBrewer"))
{
   quick.map <- function(spdf,var,legend.title,main.title) 
   {
     x <- spdf@data[,var]
     cut.vals <- pretty(x)
     x.cut <- cut(x,cut.vals)
     cut.levels <- levels(x.cut)
     cut.band <- match(x.cut,cut.levels)
     colors <- brewer.pal(length(cut.levels), "YlOrRd")
     colors <- rev(colors)
     par(mar=c(1,1,1,1))
     plot(ewoutline,col="olivedrab",bg="lightblue1")
     title(main.title)
     plot(spdf,add=TRUE,col=colors[cut.band],pch=16)
     legend("topleft",cut.levels,col=colors,pch=16,bty="n",title=legend.title)
  }
  quick.map(localstats1$SDF, "PurPrice_LM", "1000's Uk Pounds", 
  "Geographically Weighted Mean")
  par(mfrow = c(1, 2))
  quick.map(localstats1$SDF, "PurPrice_LSKe", "Skewness Level", "Local Skewness")
  quick.map(localstats1$SDF, "PurPrice_LSD", "1000's Pounds", "Local Standard Deviation")
  #Exploring Non-Stationarity of Relationships
  quick.map(localstats1$SDF, "Corr_PurPrice.FlrArea", expression(rho), 
  "Geographically Weighted Pearson Correlation")
  #Robust, Quantile Based Local Summary Statistics
  localstats2 <- gwss(houses.spdf, vars = c("PurPrice", "FlrArea"), 
  bw = 50000, quantile = TRUE)
  quick.map(localstats2$SDF, "PurPrice_Median", "1000 UK Pounds", 
  "Geographically Weighted Median House Price")
}
}