radon_vary_intercept_a.stan

data {
  int<lower=0> J;
  int<lower=0> N;
  array[N] int<lower=1, upper=J> county;
  vector[J] u;
  vector[N] x;
  vector[N] y;
}
parameters {
  vector[J] a;
  real b;
  vector[2] beta;
  real g_0;
  real g_1;
  real<lower=0, upper=100> sigma_a;
  real<lower=0, upper=100> sigma_y;
}
transformed parameters {
  vector[J] a_hat;
  vector[J] e_a;
  vector[N] y_hat;
  
  for (j in 1 : J) {
    a_hat[j] = 100 * g_0 + 100 * g_1 * u[j];
  }
  e_a = a - a_hat;
  
  for (i in 1 : N) {
    y_hat[i] = a[county[i]] + x[i] * b * 100;
  }
}
model {
  g_0 ~ normal(0, 1);
  g_1 ~ normal(0, 1);
  
  sigma_a ~ uniform(0, 100);
  a ~ normal(a_hat, sigma_a);
  
  b ~ normal(0, 1);
  
  sigma_y ~ uniform(0, 100);
  y ~ normal(y_hat, sigma_y);
}