########### RUN THE FOLLOWING TO GENERATE DATA ##############
n.groups <- 3
n.sample <- 10 
n <- n.groups* n.sample
x <- rep(1:n.groups, rep(n.sample, n.groups))
pop <- factor(x, labels = c("Montpellier","Paris","Leon"))
shrub_M <- sort(runif(n.sample,0,1))
shrub_P <- sort(runif(n.sample,0,1))
shrub_L <- sort(runif(n.sample,0,1))
shrub <- c(shrub_M,shrub_P,shrub_L)
Cams <- round(runif(n,10,50))
Xmat <- model.matrix(~pop*shrub)
#print(Xmat,dig=2)
beta.vec <- c(-4,1,2,1,2,6)
lin.pred <- Xmat[,]%*%beta.vec
exp.p <- exp(lin.pred)/(1+exp(lin.pred))
Caps <- rbinom(n=n, size=Cams, prob=exp.p)
rodents <- as.data.frame(cbind(shrub,Caps,Cams,pop))
rodents$pop <- factor(rodents$pop)
levels(rodents$pop) <-  c("Montpellier","Paris","Leon")
#### Do not chage anything above this line 


#######  Data for students  ########
# Caps == camera traps with capture
# Cams == total number of camera traps