model1_ppc.stan

data{
    int N; // no of samples
    array[N] real distance;   // distances
    array[N] real meal_preparation_time;
    array[N] int traffic_level;
}

generated quantities {
   real distance_coeff = normal_rng(0, 0.3);
   real meal_prep_coeff = normal_rng(0, 0.3);
   real mean = normal_rng(3, 0.1);

   array[4] real traffic_level_coeff;
   traffic_level_coeff[1] = normal_rng(0, 0.3);
   traffic_level_coeff[2] = normal_rng(0, 0.3);
   traffic_level_coeff[3] = normal_rng(0, 0.3);
   traffic_level_coeff[4] = normal_rng(0, 0.3);

   array[N] real mu;
   real sigma = exponential_rng(0.5);
   array[N] real delivery_times;

   for (i in 1:N){
      mu[i] = exp(distance_coeff*distance[i] + traffic_level_coeff[traffic_level[i]]+meal_prep_coeff*meal_preparation_time[i]+mean);
      delivery_times[i] = inv_gamma_rng(pow(mu[i], 2) / pow(sigma, 2) + 2, pow(mu[i],3) / pow(sigma, 2) + mu[i]);
   }
}