Andrew Gelman and his blog readers followed-up with the previous discussion (link here) on his methods to address issues about causal inference and transportability of causal effects based on his “hierarchical modeling” framework, and I just posted my answer.
This is the general link for the discussion:
Here is my answer:
In the past week, I have been engaged in a discussion with Andrew Gelman and his blog readers regarding causal inference, selection bias, confounding, and generalizability. I was trying to understand how his method which he calls “hierarchical modelling” would handle these issues and what guarantees it provides. Unfortunately, I could not reach an understanding of Gelman’s method (probably because no examples were provided).
Still, I think that this discussion having touched core issues of scientific methodology would be of interest to readers of this blog, the link follows:
Previous discussions took place regarding Rubin and Pearl’s dispute, here are some interesting links:
If anyone understands how “hierarchical modeling” can solve a simple toy problem (e.g., M-bias, control of confounding, mediation, generalizability), please share with us.
Antonio Forcina writes:
I have tried to read Judea and Ilya's paper on effect of treatment on the treated which sound much more general than anything else I have read on the subject before. Unfortunately I was unable to follow their proof and could not find an instance where the ETT effect is identifiable. The only instance where I new that ETT was identifiable is with an instrumental variable under certain restrictions, instead I imagine that identifiability here means without restrictions other than those encoded in the DAG.The most clear treatment of the subject I new until now is in a paper by Hernan and Robins in Epidemiology 2006; and I do not understand why the discussion on Forcina's paper by Robins, Vander Weele and RIchardson is so popular.
The parameter identification method described in Section 5.3.1 rests on two criteria: (1) The single door criterion of Theorem 5.3.1, and the back-door criterion of Theorem 5.3.2. This method may require appreciable bookkeeping in combining results from various segments of the graph. Is there a single graphical criterion of identification that unifies the two Theorems and thus avoids much of the bookkeeping involved?