n_Section 18 (ST-CAR model)

# install.packages( c("CARBayesST", "CARBayesdata", "RColorBrewer", "spdep", "sf"))
library(CARBayesST)
library(CARBayesdata)
library(RColorBrewer)
library(spdep)
library(sf)

##### pollutionhealthdata 
data(pollutionhealthdata)
data(GGHB.IG)
W.nb   	<- poly2nb(GGHB.IG)
W      	<- nb2mat(W.nb, style = "B")
pollutionhealthdata[1:4,]

##### Spatiotemporal CAR model
formula	<- observed ~ offset(log(expected)) + jsa + price + pm10
model   <- ST.CARar(formula = formula, family = "poisson", 
                    data = pollutionhealthdata, AR=1, W = W, 
                    burnin = 2000, n.sample = 50000)
model

##### Plot the predicted value in 2008 (disease mapping)
pollutionhealthdata$predCAR<-model$fitted.values
dat	    <- merge(x=GGHB.IG, y=pollutionhealthdata, by="IG", 
                 all.x=FALSE, duplicateGeoms = TRUE) 
dat2    <- st_as_sf(dat)

year    <- 2008
dat2_sub<- dat2[dat2$year==year,]
nc	    <- 11
breaks  <- seq(10, 200, len=nc+1)
pal     <- rev(brewer.pal(nc, "RdYlBu"))
plot(dat2_sub[, c("observed", "predCAR")], pal=pal, breaks=breaks, axes=TRUE, lwd=0.1)

##### Spatiotemporal CAR model with estimation of spatially dependent neighborhoods
model2  <- ST.CARadaptive(formula = formula, family = "poisson",
                          data = pollutionhealthdata, W = W, burnin = 5000, n.sample = 50000)
model2

##### Plot the estimated spatially dependent neighborhoods
Wmedian <-model2$localised.structure$Wmedian
Wmedian[is.na(Wmedian)]<-0
Wmedian2<- ifelse(Wmedian>0, 0.8,0)
West    <- mat2listw(Wmedian2)	
coords  <-st_coordinates(st_centroid(dat2_sub))
plot(st_geometry(dat2_sub), border="grey")
plot(West, coords, add = TRUE, col="red",cex=0.01,lwd=1,xlim=xlim,ylim=ylim)