# N is number of observation
# Lmic[i] is the log of MIC value of ith obsevation
# dnorm means it is a normal distributed variable
# Lmu[i] is the mean of Lmic[i]
# tauLmic is 1/variance(Lmic)
# lower[i] and upper[i] are lower and upper bound for Lmic[i] 
# alpha0 is intercept term
# alpha.type is the coefficient of type effect


model {

	for (i in 1:N) 
		{		
		Lmic[i] ~ dnorm(Lmu[i],tauLmic)I(lower[i], upper[i])
		Lmu[i] <- alpha0 + alpha.type[type[i]] +alpha.visit*visit[i]	
                resid[i] <- Lmic[i] - Lmu[i]		
		}

# Prior Distributions for alpha0  

		alpha0 ~ dnorm(0, 0.1)


# Prior Distributions for alpha.type

		alpha.type[1]<-0
		alpha.type[2]~ dnorm(0, 0.1)


# Prior Distributions for alpha.visit
                
		alpha.visit~dnorm(0, 0.1)


# Prior Distributions for tauLmic
	
		tauLmic ~ dgamma(0.1, 0.01)
		sigmaLmic <- 1 / sqrt(tauLmic)

#Prediction: type 0 is the vegetarian diet, type 1 is the commercial diet

	       pred.type0.visit1<- alpha0 + alpha.type[2] + alpha.visit
               pred.type0.visit2<- alpha0 + alpha.type[2] + alpha.visit*2
	       pred.type0.visit3<- alpha0 + alpha.type[2] + alpha.visit*3
               pred.type0.visit4<- alpha0 + alpha.type[2] + alpha.visit*4
	       pred.type0.visit5<- alpha0 + alpha.type[2] + alpha.visit*5
               pred.type1.visit1<- alpha0 + alpha.type[1] + alpha.visit
	       pred.type1.visit2<- alpha0 + alpha.type[1] + alpha.visit*2
               pred.type1.visit3<- alpha0 + alpha.type[1] + alpha.visit*3
	       pred.type1.visit4<- alpha0 + alpha.type[1] + alpha.visit*4
               pred.type1.visit5<- alpha0 + alpha.type[1] + alpha.visit*5
	}