multinomial logistic regression model in stan

multinomial-LR.stan

data { 
  int J; // number of predictors or features
  int K; // outcome classes
  int N; 
  array[N] int y;
  matrix[N, J] X;
}
parameters {
  matrix[J, K-1] beta; // number of predictor * number of classes-1
}
transformed parameters {
  // last class as the reference
  matrix[J, K] beta_new = append_col(beta, rep_vector(0, J));
}
model {
  matrix[N, K] Z = X * beta_new;
  to_vector(beta_new) ~ normal(0, 10); 
  for (n in 1:N) {
    // y[n] ~ categorical(softmax(x[n] * beta));
    y[n] ~ categorical_logit(Z[n]');
  } 
}