// corresponding to JAGS example 
// in R package BUGSExamples 
// [install.packages("BUGSExamples", repos="http://R-Forge.R-project.org")]
// 

data {
  int<lower=0> N;
  int<lower=0> T;
  array[N, T] int<lower=0> y;
  array[N] int<lower=0> Trt;
  array[T] int<lower=0> V4;
  vector[N] log_Base4;
  vector[N] log_Age;
  vector[N] BT;
  real log_Age_bar;
  real Trt_bar;
  real BT_bar;
  real V4_bar;
  real log_Base4_bar;
}
transformed data {
  vector[T] V4_c;
  vector[N] log_Base4_c;
  vector[N] log_Age_c;
  vector[N] BT_c;
  vector[N] Trt_c;
  log_Base4_c = log_Base4 - log_Base4_bar;
  log_Age_c = log_Age - log_Age_bar;
  BT_c = BT - BT_bar;
  for (i in 1 : T) {
    V4_c[i] = V4[i] - V4_bar;
  }
  for (i in 1 : N) {
    Trt_c[i] = Trt[i] - Trt_bar;
  }
}
parameters {
  real a0;
  real alpha_Base;
  real alpha_Trt;
  real alpha_BT;
  real alpha_Age;
  real alpha_V4;
  array[N] real b1;
  array[N] vector[T] b;
  real<lower=0> sigmasq_b;
  real<lower=0> sigmasq_b1;
}
transformed parameters {
  real<lower=0> sigma_b;
  real<lower=0> sigma_b1;
  sigma_b = sqrt(sigmasq_b);
  sigma_b1 = sqrt(sigmasq_b1);
}
model {
  a0 ~ normal(0, 100);
  alpha_Base ~ normal(0, 100);
  alpha_Trt ~ normal(0, 100);
  alpha_BT ~ normal(0, 100);
  alpha_Age ~ normal(0, 100);
  alpha_V4 ~ normal(0, 100);
  sigmasq_b1 ~ inv_gamma(.001, .001);
  sigmasq_b ~ inv_gamma(.001, .001);
  b1 ~ normal(0, sigma_b1);
  for (n in 1 : N) {
    b[n] ~ normal(0, sigma_b);
    y[n] ~ poisson_log(a0 + alpha_Base * log_Base4_c[n]
                       + alpha_Trt * Trt_c[n] + alpha_BT * BT_c[n]
                       + alpha_Age * log_Age_c[n] + b1[n] + alpha_V4 * V4_c
                       + b[n]);
  }
}
generated quantities {
  real alpha0;
  // re-calculate intercept on original scale:
  alpha0 = a0 - alpha_Base * log_Base4_bar - alpha_Trt * Trt_bar
           - alpha_BT * BT_bar - alpha_Age * log_Age_bar - alpha_V4 * V4_bar;
}