#JAGS model for Bayesian analysis 
#Pedro 05/25/2015

  model {
    
    ## Priors for fixed effects
    Betas1 ~ dnorm(0,0.0001)  
    Betas2 ~ dnorm(0,0.0001) 
    
    ## Priors for random intercepts & slopes
    for (k in 1:Npop) {
    alpha.p[k] ~ dnorm(0,tau.plot.a)
    beta.p[k] ~ dnorm(0,tau.plot.b)}
    
    ## Priors for random error 
    tau.plot.a <- 1/(sigma.plot.a*sigma.plot.a)
    tau.plot.b <- 1/(sigma.plot.b*sigma.plot.b)
    tau.eps <- 1/(sigma.eps*sigma.eps)
    sigma.plot.a ~ dunif(0.001,10)
    sigma.plot.b ~ dunif(0.001,10)
    sigma.eps ~ dunif(0.001,10)
    
    ## Likelihood
    for(i in 1:N){    
    Y[i] ~ dnorm(mu[i],tau.eps) 
    mu[i] <- eta[i] 
    eta[i] <- Betas1 + (Betas2 + beta.p[pp[i]]) *X[i] + alpha.p[pp[i]]}
  
}