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

  model {
    
    ## Priors fixed
    Betas1 ~ dnorm(0,0.0001)  
    Betas2 ~ dnorm(0,0.0001)
    
    for (j in 1:Nstems) { 
      Betas3[j] ~ dnorm(0,0.0001)
    } 
    
    for (k in 1:Ntsf) { 
      Betas4[k] ~ dnorm(0,0.0001)
    } 
    
    for (j in 1:Ntsf) { 
      for (k in 1:Nstems) {  
      Betas5[j,k] ~ dnorm(0,0.0001)
      } }
      
    ## Priors random intercepts
    for (j in 1:Nyear) { 
        alpha.y[j] ~ dnorm(0,tau.year.a)
        beta.y[j] ~ dnorm(0,tau.year.b)
      } 
    
    for (i in 1:Nyear) { 
    for (k in 1:Npop) {
      alpha.p[k,i] ~ dnorm(0,tau.plot.a)
      beta.p[k,i] ~ dnorm(0,tau.plot.b)
      } }
    
    ## priors for random
    tau.plot.a <- 1/(sigma.plot.a*sigma.plot.a)
    tau.plot.b <- 1/(sigma.plot.b*sigma.plot.b)
    tau.year.a <- 1/(sigma.plot.a*sigma.year.a)
    tau.year.b <- 1/(sigma.plot.b*sigma.year.b)
    tau.eps <- 1/(sigma.eps*sigma.eps)
    sigma.eps ~ dunif(0.001,10)
    sigma.plot.a ~ dunif(0.001,10)
    sigma.plot.b ~ dunif(0.001,10)
    sigma.year.a ~ dunif(0.001,10)
    sigma.year.b ~ 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],yy[i]] + beta.y[yy[i]])*X[i] + alpha.p[pp[i],yy[i]] +alpha.y[yy[i]] +
      Betas3[stem[i]] + Betas4[tsf[i]] + Betas5[tsf[i],stem[i]]
    }
  
  }