Asking Clear Questions and Building Graphs

[@yulinliu850]

🎉❤👍

[@harinathan5778]

In the voting example, let's say we didn't/couldn't find a variable like M to use. If we just proceeded by controlling for for P and E, couldn't we say that the resulting analysis gives the ACE for A "for people who use the website?" In other words, that it would only apply to this sub-population?

[@lesliemyint1865]

Because S is inherently conditioned on (there's nothing we can do about this because that's just the data we have), our ACE estimate will indeed only apply to the subpopulation of people who use the website. But because of the collider stratification bias (conditioning on S) even this subpopulation ACE estimate will be biased. That is, even if our goal is just to estimate the causal effect of treatment for people who use the website, we will have bias in estimating this effect. (This is sometimes referred to as a lack of internal validity.) In order for the subpopulation ACE estimate to not be biased, we need to have some way of dealing with the A S Y noncausal path. (Perhaps we can find a proxy for one of the unmeasured variables.)