# JAGS_model.txt : JAGS model for ordinal regression 

model{ 
	# main loop over N observations 
	for(i in 1:N){ 
		# linear predictor (intercept excluded for	identifiability)
		omega[i] <- beta[1]*x[i,1] +
		beta[2]*x[i,2] + beta[3]*x[i,3] + beta[4]*x[i,4] +
		beta[5]*x[i,5] + beta[6]*x[i,6] + beta[7]*x[i,7] +
		beta[8]*x[i,8] + psi[encId[i]] 

	# cumulative logistic probabilities 
	logit(G[i,1]) <- tau[1] - omega[i] 
	p[i,1] <- G[i,1] 
	for(j in 2:4){ 
		logit(G[i,j]) <- tau[j] - omega[i] 
		p[i,j] <- G[i,j] - G[i,j-1] 
	} 
	p[i,5] <- 1 - G[i,4]

	# categorical distribution for y 
	# p’s for each observation sum to 1 across 5 categories 
	y[i] ~ dcat(p[i,1:5]) 

	# posterior predictive 
	yrep[i] ~ dcat(p[i,1:5]) 
} 

	# Priors 
	# betas 
	beta[1:8] ~ dmnorm(Mu[],Sig[,]) 

	# random effects across 12 enclosures 
	for(k in 1:12){ 
	psi[k] ~ dnorm(0.0,prec) 
	}

	# precision from uniform-prior sd 
	prec <- pow(sigma,-2) 
	sigma ~ dunif(0,5) 

	# ordered cutpoints 
	for(j in 1:4){ 
	tau0[j] ~ dnorm(0,0.01) 
	} 
	tau[1:4] <- sort(tau0) 
}