Hierarchical Model for Publication Bias

Modeling
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21

Apologies. Won’t happen again .

22

Hi @Ole_Rogeberg, thank you very much for your reply. To me this seems to be a truncated distribution problem, for which the model I am doing should theoretically correct for it, at the cost of assuming the process of truncation.

I am still not super sure I understand why the normalization constant should be study specific, that is not the case for a truncation process, in which you correct the whole likelihood. Moreover, looking at your paper, in the model section you also model the likelihood with a reweighting scheme and normalize by an overall constant, so I am slightly confused.

Would you be willing to share your updated code, so I can compare it to the old one?

I am also a bit confused by the role of

type_pub_prob[i] = softmax(temp_prob_raw[, i]);

since you never use it again in the model. If I understand correctly your model, in this section

model {
  global_mu ~ normal(0, 1);
  mu_sigma ~ normal(0,1);
  rel_obsprob ~ gamma(1, 2);
  //model
  for (i in 1:N){
    real temp_norm;
    real temp_sd_both = sqrt(se[i]^2 + mu_sigma^2);
    temp_norm = log_sum_exp(temp_prob_raw);
    // Probability of observing a study with the observed type given the standard error
    if (results_type[i] == 1){
      target += log_rel_obsprob[1] + normal_lpdf(y[i] | global_mu, temp_sd_both) - temp_norm;
    } else if (results_type[i] == 2){
      target += log_rel_obsprob[2] + normal_lpdf(y[i] | global_mu, temp_sd_both) - temp_norm;
    } else {
      target += normal_lpdf(y[i] | global_mu, temp_sd_both) - temp_norm;
    }
  }
}

This part temp_norm = log_sum_exp(temp_prob_raw), should actually be temp_norm = log_sum_exp(type_pub_prob), am I correct in thinking that?

23

No worries, and thanks for being understanding.