radon_redundant.stan

data {
  int<lower=0> J;
  int<lower=0> N;
  array[N] int<lower=1, upper=J> county;
  vector[N] y;
}
parameters {
  vector[J] eta;
  real mu;
  real<lower=0, upper=100> sigma_eta;
  real<lower=0, upper=100> sigma_y;
}
transformed parameters {
  vector[J] eta_adj;
  real mean_eta;
  real mu_adj;
  vector[N] y_hat;
  
  mean_eta = mean(eta);
  mu_adj = 100 * mu + mean_eta;
  eta_adj = eta - mean_eta;
  for (i in 1 : N) {
    y_hat[i] = 100 * mu + eta[county[i]];
  }
}
model {
  mu ~ normal(0, 1);
  sigma_eta ~ uniform(0, 100);
  sigma_y ~ uniform(0, 100);
  eta ~ normal(0, sigma_eta);
  y ~ normal(y_hat, sigma_y);
}