model{
  ## Likelihood
  for(i in 1:n){
    y[i] ~ dpois(lambda.hacked[i])
    lambda.hacked[i] <- lambda[i]*(1-zero[i]) + 1e-10*zero[i]
    lambda[i] <- exp(mu.count[i])
    mu.count[i] <- beta00 + beta1*x[i] + beta2*r2[i] +beta3*r3[i] +beta4*r4[i]
    
    ## Zero-Inflation
    zero[i] ~ dbern(pi[i])
    pi[i] <- ilogit(mu.binary[i])
    mu.binary[i] <- alpha00 + alpha11*x[i]
  } 
  ## Priors
  beta00 ~ dnorm(0,0.0001) 
  beta1 ~ dnorm(0,0.0001) 
  beta2 ~ dnorm(0,0.0001) 
  beta3 ~ dnorm(0,0.0001)
  beta4 ~ dnorm(0,0.0001)
  alpha00 ~ dnorm(0,0.0001) 
  alpha11 ~ dnorm(0,0.0001) 
  
}