#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] ~ dbern( mu[i] )
    mu[i] <- eta[i] 
    eta[i] <- 1/(1+exp(-(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]])))
  }
  
}