Examples for modeling selection effect, non-response?

[blakeobeans]

I was listening to the Bayesian Statistics Podcast, episode #6 and @betanalpha talked about using Stan to adjust for selection effects in data. I am wondering if there are any examples or case studies of this floating around. Much appreciated, thanks!

[bgoodri]

If you search on Discourse for Heckman, there are some good threads, such as this one:

Heckman selection model code + simulation

Here’s a Stan program that implements the Heckman likelihood and fits the program to fake data. It recovers the parameters well. I haven’t yet fitted it to repeated simulated datasets though. EDIT: The code below has an error in the likelihood, which @RachaelMeager caught in her post below (link). Follow the link for the explanation, the correct code, and an extension! The likelihood contribution for observed units below should be: log(Phi(sqrt(1 - rho^2)^(-1)*(mu_y2[n_pos[n]] …

[betanalpha]

Examples, and the vocabulary they use, will vary pretty strongly by field so you may want to start looking in a field in which you are comfortable. One-dimensional truncation is perhaps the simplest selection effect and there are example in the Stan manual. See also the last example in https://betanalpha.github.io/assets/case_studies/principled_bayesian_workflow.html.