#--------------------------------------------------------------------
# Code for Article
#
# Spatial patterns of livestock activity on heterogeneous subalpine
# pastures reveal distinct responses to environment and management
# 
# H. Homburger, A. Lüscher, M. Scherer-Lorenzen and M.K. Schneider
#---------------------------------------------------------------------

#source("http://www.math.ntnu.no/inla/givemeINLA.R") #to install INLA 

library(sp)
library(INLA)
inla.setOption("enable.inla.argument.weights", TRUE) #Needed for weighted regression

#Read-in data
setwd("path/to/data")
grid <- read.table("exampleData.txt",sep="\t",h=T) #read dataser
coordinates(grid) <- ~X+Y 										     #SpatialPointsDataFrame
gridded(grid) <- TRUE											     #SpatialGridDataFrame spatial data is gridded
grid <- as(grid, "SpatialGridDataFrame") # convert to full grid

#Visualise
par(mfrow=c(3,5),mar=c(0,0,5,0))
for(i in 1:ncol(grid)) {
	image(grid[names(grid)[i]], col=rev(gray.colors(20)))
	title(main=names(grid)[i],line=1)}

# Set up INLA
Yvar <- "G" #Choose G, R or W
n.cells <- nrow(grid)
cell.area <- as.numeric(grid@grid@cellsize[1]^2)
cell.dims <- grid@grid@cells.dim
grid$I <- grid$J <- grid$L <- 1:n.cells
grid$E <- cell.area
grid$count <- grid@data[,paste("count",Yvar, sep="_")]
grid$weight <- grid@data[,paste("weight",Yvar, sep="_")]

grid$logdist_wat <- log(grid$dist_wat)
grid$logdist_shed <- log(grid$dist_shed)

stand <- function(x) (x-mean(x,na.rm=T))/sd(x,na.rm=T) 	# Standartization function
vars <- c("Z","slope","stocking","logdist_wat","logdist_shed","insolat")
grid@data[,paste(vars,"S",sep="")] <- apply(grid@data[,vars],2,stand)

hyper.unst <- list(prec=list(param=c(0.5, 0.00149))) # Following Fong, Rue and Wakefield (2009), Example 5.2, and Papoila et al (2014) 

# Define limit for upper standard deviation
alpha <- 0.001 #as in Sorbye and Rue (2012) and Papoila et al (2014)
U = 0.5
a <- 1
b <- sapply(U, function(u) u^2*qgamma(alpha, shape=a,rate=1)) #Sigma^2ref is 0 since we use scale.model=T and is same for all GRMFs (see Sorbye 2013)
hyper.prec <- list(prec=list(param=c(a,b)))

# Define the model
formula <- count ~ 1 + slopeS + veg + logdist_shedS + logdist_watS + stockingS + insolatS +
		f(Zs, model="rw1", scale.model=T, hyper=hyper.prec) +
		f(I, model="rw2d", nrow=cell.dims[1], ncol=cell.dims[2], scale.model=TRUE, hyper=hyper.prec) +   #structured spatial error
		f(J, model="iid", hyper=hyper.unst)

#Fitting the model takes about 2 mins, be patient!
M <- inla(formula, data=grid@data, family="zeroinflatednbinomial0", 
	weights=grid$weight, control.inla = list(strategy = "gaussian", int.strategy = "eb"),
	control.results=list(return.marginals.random=F, return.marginals.predictor=F),)

summary(M) #to see the parameter estimates

grid$f.spat <- M$summary.random$I$mean #Extract the spatial effect
image(grid["f.spat"])
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