j_Section 13 (GWR)

# install.packages( c("GWmodel", "sp" ) )
library(GWmodel)
library(sp)

##### Meuse data
data(meuse)
meuse$ffreq2 <- ifelse(meuse$ffreq ==2, 1, 0)
meuse$ffreq3 <- ifelse(meuse$ffreq ==3, 1, 0)
meuse$soil2  <- ifelse(meuse$soil  ==2, 1, 0)
meuse$soil3  <- ifelse(meuse$soil  ==3, 1, 0)
meuse[1:5,]

##### Geographically weighted regression
formula  <-log(zinc) ~ soil2 + soil3 + ffreq2 + ffreq3 + dist
meuse_sf <-st_as_sf(meuse, coords = c("x", "y"), crs = 28992)
meuse_sp <-as_Spatial(meuse_sf)
bwE      <-bw.gwr(formula, approach="CV", data=meuse_sp, kernel = "exponential")
res      <-gwr.basic(formula,data=meuse_sp, bw=bwE, kernel = "exponential")
res

##### Statistical significance of the coefficients
res$SDF@data[1:5,]
pval       <-gwr.t.adjust(res)
pval$SDF@data[1:5,]

##### Plot estimated coefficients 
beta       <-res$SDF@data[,1:6]
names(beta)<-paste(names(beta),"_coef",sep="")
meuse_sf   <-cbind(meuse_sf,beta)
plot(meuse_sf[,"soil2_coef"],pch=20,axes=TRUE)

##### Meuse grid data (predicted sites) 
data(meuse.grid)
meuse.grid$ffreq2	<- ifelse(meuse.grid$ffreq ==2, 1, 0)
meuse.grid$ffreq3	<- ifelse(meuse.grid$ffreq ==3, 1, 0)
meuse.grid$soil2 	<- ifelse(meuse.grid$soil  ==2, 1, 0)
meuse.grid$soil3 	<- ifelse(meuse.grid$soil  ==3, 1, 0)
meuse.grid_sf 	<-st_as_sf(meuse.grid, coords = c("x", "y"), crs = 28992)
meuse.grid_sp 	<-as_Spatial(meuse.grid_sf)

##### Spatial prediction
pred  <- gwr.predict(formula,data=meuse_sp, bw=bwE, kernel = "exponential", predictdata=meuse.grid_sp)
summary(pred$SDF)

##### Plot predicted values and their variances
meuse.grid_sf   <-cbind(meuse.grid_sf,pred$SDF)
plot(meuse.grid_sf[,"prediction"],pch=20,axes=TRUE)
plot(meuse.grid_sf[,"prediction_var"],pch=20,axes=TRUE)

##### Plot estimated coefficients 
plot(meuse.grid_sf[,"soil2_coef"],pch=20,axes=TRUE)