In my Mixtape, I tried to convey an RDD via a DAG and the more I look at it, the more problematic it looks. First, the discontinuity (c0) is presented alongside the ray from X to D, but c0 is not a variable. It’s a value.
Second nothing in this Dag explains the identifying assumption for RDD which is continuity and therefore a functional form type of assumption on the potential outcomes.
Now the reason I did it this way was this: RDD is selection on observables, therefore we’d expect the DAG to be one addressing confounding, which is the form of this DAG. I was therefore thinking maybe the running variable could be blocked on which is done via c0?
But even then you still wouldn’t see continuity. And that’s really the problem - am I actually adding value by presenting RDD as a DAG if I can’t actually understand the identifying assumptions? FYI @EpiEllie , @paulgp , @PHuenermund , @eliasbareinboim , @yudapearl , @Jabaluck
Now I think maybe what u really want is a Single World Intervention Graph or SWIG. U specify both actual observed and hypothetical “intervened upon” values of a variable, causes of actual & intervened on nodes can differ, & counterfactual is made explicit. citeseerx.ist.psu.edu/viewdoc/downlo…
The SWIG for your first DAG might look something like this...
But I’m not sure whether the dashed arrow should be there — typically when the intervention depends on a covariate we include it, but based on this SWIG I’m not sure the counterfactual is identified 🤔
The key assumption of regression discontinuity is that conditional on X being very near c0, whether X is above or below c0 has no (or just an extremely weak) direct effect on Y except through d. It's the IV exclusion restriction w/ X as IV conditional on X being in a narrow range
This conditioning on X being in a narrow range is missing from all of these DAGs/SWIGs
To the best of my knowledge, a DAG encodes causal relationships, not distributional assumption. Since the IV causes the exposure, all you need is to draw a DAG that goes from IV->E->Y without any back door paths from IV to Y. Right? Or am I missing something? @EpiEllie
Yeah, that’s eventually where I got to as well, with the additional feature of showing that the identifiability comes from restricting on a narrow range of the “IV”twitter.com/epiellie/statu…