radon_vary_si.stan

data {
  int<lower=0> N;
  array[N] int<lower=1, upper=85> county;
  vector[N] x;
  vector[N] y;
}
parameters {
  vector[85] a1;
  vector[85] a2;
  real mu_a1;
  real mu_a2;
  real<lower=0, upper=100> sigma_a1;
  real<lower=0, upper=100> sigma_a2;
  real<lower=0, upper=100> sigma_y;
}
transformed parameters {
  vector[N] y_hat;
  
  for (i in 1 : N) {
    y_hat[i] = a1[county[i]] + a2[county[i]] * x[i];
  }
}
model {
  mu_a1 ~ normal(0, 1);
  a1 ~ normal(mu_a1, sigma_a1);
  mu_a2 ~ normal(0, 1);
  a2 ~ normal(0.1 * mu_a2, sigma_a2);
  
  y ~ normal(y_hat, sigma_y);
}