// Multivariate Regression Example
// Taken from stan-reference-2.8.0.pdf p.66

data {
  int<lower=0> N;             // num individuals
  int<lower=1> K;             // num ind predictors
  int<lower=1> J;             // num groups
  int<lower=1> L;             // num group predictors
  int<lower=1,upper=J> jj[N]; // group for individual
  matrix[N,K] x;              // individual predictors
  row_vector[L] u[J];         // group predictors
  vector[N] y;                // outcomes
}
parameters {
  corr_matrix[K] Omega;       // prior correlation
  vector<lower=0>[K] tau;     // prior scale
  matrix[L,K] gamma;          // group coeffs
  vector[K] beta[J];          // indiv coeffs by group
  real<lower=0> sigma;        // prediction error scale
}
model {
  tau ~ cauchy(0,2.5);
  Omega ~ lkj_corr(2);
  to_vector(gamma) ~ normal(0, 5);
  {
    row_vector[K] u_gamma[J];
    for (j in 1:J)
      u_gamma[j] <- u[j] * gamma;
    beta ~ multi_normal(u_gamma, quad_form_diag(Omega, tau));
  }
  {
    vector[N] x_beta_jj;
    for (n in 1:N)
      x_beta_jj[n] <- x[n] * beta[jj[n]];
    y ~ normal(x_beta_jj, sigma);
  }
}

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