I’m trying to parse the following two views with respect to group effects in Bayesian models (NB: For what it’s worth I default to brms, hence the tag):
- The first view is that groups can be accounted for using group-level effects, as per this comment rather than the clustered standard errors that are used in frequentist models.
- The second view is “… a Bayesian analogue of estimating equations and the sandwich estimator has been an open problem for some time” (Szpiro, Rice, and Lumley 2010)
So, my two related questions are:
- Which view is correct and why?
- If the inclusion of group-level effects in Bayesian models doesn’t fully address the issue of clustering, then what is the best way to address them (preferably in brms)?
Thanks in advance and let me know if people think this question is better put to SO.
Both views are correct in this case. The two approaches are simply different methods for handling clustered data. The group effects approach here also isn’t unique to a Bayesian framework.
The cluster-robust standard errors handles the non-independence by adjusting the standard errors- but otherwise returning the same estimates. Whereas the group effects approach handles the non-independence by including it in the model.
The linked forum post was simply saying that the concept of adjusting standard errors does not yet have a Bayesian analogue, and so the best approach is to use group effects to handle the non-independence
Thanks so much for the explanation Andrew. That does make sense.
Are you aware of how the method outlined in Szpiro, Rice, and Lumley 2010 might be implemented in brms, or is that a bridge too far for the package? Appreciate that q may be better left to Christian B.