I have recently been reading more on graphical causal models and the term collider often comes up. I am wondering if there exists an interpretation for what it is in the potential outcomes framework.


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I find the definition in Hernan & Robins's forthcoming book (Causal Inference pg 101) to be useful

[Colliders are] a common effect of two other variables in the diagram ... We will use the term selection bias to refer to all biases that arise from conditioning on a common effect of two variables, one of which is either the treatment or a cause of treatment, and the other is either the outcome or a cause of the outcome.

There several example causal diagrams show how it is easier to approach "colliders" from a graphical persepective. You can also frame colliders in terms of single-world intervention graphs (SWIG) which explicitly links the causal diagram and potential outcome approach.

Let $A$ be the treatment of interest and $Y(a)$ be the potential outcome $Y$ under treatment $A=a$. Therefore, a collider would be $C$ would be written in a SWIG as $C(a, Y(a))$, which indicates it caused by $A$ and $Y(a)$ (i.e. a descendant of both $A$ and $Y(a)$). Conditioning on the collider $C$ in the analysis introduces selection bias, as defined by Hernan and Robins

  • $\begingroup$ Are you aware of any terms used in the Rubin potential outcomes framework that is equivalent to a collider? It seems it doesn't exist in the Rubin framework. thanks. $\endgroup$
    – user321627
    Oct 15, 2019 at 22:30
  • $\begingroup$ I'm unaware of any discussion outside some mentions of M-bias (a particular example structure of colliders). This blog post (and the link in it) may have some useful discussion statmodeling.stat.columbia.edu/2009/07/05/disputes_about $\endgroup$
    – pzivich
    Oct 16, 2019 at 11:39

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