  /* multinomial-logit log-PMF
   * Args:
   *   y: array of integer response values
   *   mu: vector of category logit probabilities
   * Returns:
   *   a scalar to be added to the log posterior
   */
   real multinomial_logit2_lpmf(int[] y, vector mu) {
     return multinomial_lpmf(y | softmax(mu));
   }
