How to calculate log_lik in generated quantities of a multivariate regression model

Interfaces CmdStan
,
6

Yes, here it is. It is just a linear regression with hierarchical \beta and I wrote the log_lik as you suggested

data {
  int<lower=0> n_group;
  int<lower=0> n_indiv;      
  int<lower=0> n_obs;      
  int<lower=0> n_des;
  int<lower=1, upper=n_group> idx_group[n_indiv];
  int<lower=1, upper=n_indiv> idx_indiv[n_indiv];
  array[n_indiv] vector[n_obs] Y;     
  matrix[n_obs, n_des] X;
}

parameters {
  vector[n_des] mu;
  matrix[n_group, n_des] z_group;
  matrix[n_indiv, n_des] z_indiv; 
  real<lower=0> sigma[n_indiv];
  real<lower=0> sigma_group;
  real<lower=0> sigma_indiv;
}

model {
  mu ~ normal(0,10);
  to_vector(z_group) ~ std_normal();
  to_vector(z_indiv) ~ std_normal();
  sigma_group ~ normal(0,10);
  sigma_indiv ~ normal(0,10);
  sigma ~ normal(0, 10);       
  for (n in 1:n_indiv) {
    Y[n] ~ normal_id_glm(X, 0,
    mu + sigma_group * z_group[idx_group[n]]' + sigma_indiv * z_indiv[idx_indiv[n]]',
    sigma[idx_indiv[n]]);
  }
}

generated quantities{
  vector[n_indiv * n_obs] log_lik;
    matrix[n_indiv, n_obs] temp;
      for(n in 1:n_indiv) {
        for(t in 1:n_obs) {
        temp[n, t] = normal_lpdf(Y[n, t] | X[t, ] *
        (mu + sigma_group * z_group[idx_group[n]]' + sigma_indiv * z_indiv[idx_indiv[n]]'),
        sigma[idx_indiv[n]]);
        }
      }
    log_lik = to_vector(temp);
}

This is silly but I wonder if I can write log_lik as below, it’s like calculating only one log_lik for each variate (one row of the data matrix Y) instead of two for loops calculating one log_lik per element of Y

generated quantities{
  vector[n_indiv] log_lik;
    vector[n_indiv] temp;
      for(n in 1:n_indiv) {
        temp[n] = normal_id_glm_lpdf(Y[n, ] | X, 0, 
        (mu + sigma_group * z_group[idx_group[n]]' + sigma_indiv * z_indiv[idx_indiv[n]]'),
        sigma[idx_indiv[n]]);
      }
}