1. Exquisite Tweets from @causalinf, @PedrooCava, @nickchk, @EpiEllie, @BenCharoenwong, @zshahn, @JosephVanMatre, @DavidSFink

    Woody_WongECollected by Woody_WongE

    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.

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    causalinf

    scott cunningham

    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.

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    causalinf

    scott cunningham

    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?

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    causalinf

    scott cunningham

    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

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    causalinf

    scott cunningham

  2. Can't you just write above or next to the line connecting X and Y something like "must satisfy treatment assignment criteria"? It seems like a simpler way to approach it. Oh, maybe a dotted line?

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    PedrooCava

    espaço métrico completo

  3. Could you draw it and take a picture? (Usually dotted lines are reserved for unobserved variables). Ultimately if it’s selection on observables, then it should be a design that blocks backdoor paths

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    causalinf

    scott cunningham

  4. Maybe that’s it. So you’d probably block on X. Thing is, a robust DAG will have observable and unobservable confounders and the backdoor criterion would presumably cut both off.

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    causalinf

    scott cunningham

  5. Using c_0 is indeed strange, I've used instead "X > c_0" in that spot, which is a binary variable. And isn't continuity pictured by the fact that "X > c_0" -> D -> Y is fully blocked by D?

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    nickchk

    Nick HK

  6. 1) thanks! This works much better. 2) good points about continuity. @EpiEllie would you say that that chain implies continuity (formally)?

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    causalinf

    scott cunningham

  7. 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…

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    EpiEllie

    Ellie Murray

    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 🤔

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    EpiEllie

    Ellie Murray

  8. You're living life on the edge there, with 7% left

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    BenCharoenwong

    Ben Charoenwong

  9. 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

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    zshahn

    zshahn

    This conditioning on X being in a narrow range is missing from all of these DAGs/SWIGs

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    zshahn

    zshahn

    And I'm not sure how to add it except to make a standard IV DAG with X as IV and D as treatment and say in a caption underneath that this DAG approximately describes the system only when X is near C0

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    zshahn

    zshahn

  10. The way I've thought of this is that, in its base form, the RDD is confounded because of the Cutoff <- X -> Y back door. Focusing on the narrow range is demonstrated to be necessary by the DAG as a form of adjusting for X and thus closing that back door.

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    nickchk

    Nick HK

  11. JosephVanMatre

    Joseph Van Matre

  12. Based on the SWIG, then this👇🏼also seems like it should be the required DAG. But again, not sure how to include the idea of getting around conditioning on a narrow range of X

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    EpiEllie

    Ellie Murray

  13. causalinf

    scott cunningham

  14. 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

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    DavidSFink

    David Fink

  15. 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…

    EpiEllie

    Ellie Murray

    But I think that the “IV” needs a path to the outcome too ... that’s why people want to expand the range assessed. X helps withoutcome prediction. But I don’t see how that doesn’t destroy identifiability 🤷🏼‍♀️

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    EpiEllie

    Ellie Murray