In my previous articles, we learned about confounders and colliders in observational data that hinder establishing reliable causal relationships. The solution Pearl provided is to draw causal diagrams and use the backdoor criterion to find the sets of confounders to block and leave the colliders and mediators along.
However, when dealing with confounding variables that cannot be observed or measured, it becomes difficult to estimate causality from the observational data. Coping with this issue, in Chapter 7 of “The Book of Why,” Judea Pearl introduced the do-calculus rules. These rules are particularly useful for the front-door criterion and instrumental variables. They can be used to establish causality even when unobservable confounding variables are present.
In Chapter 8, we will explore the amazing world of counterfactuals. Opening with Poet Robert Frost’s famous lines:
“And sorry I could not travel both
And be one traveler, long I stood…”
Pearl states although it’s impossible to travel both paths or step into the same rivers twice, our brains can imagine what would have happened if we had taken the other path. In order to specify and pass down the wisdom to robots, Pearl introduces the distinctions between necessary cause and sufficient cause and how to utilize Structure Causal Models to conduct counterfactual analysis systematically.
As we pass the midpoint, the chapters are getting more technical and information-intensive. In the following section, I will first discuss how to deal with unobserved confounders, unfortunately, with some math, for Rung 2 interventions. Then, I will discuss counterfactuals, a Rung 3 application.
The front-door criterion
Starting with a causal diagram that we use to understand the causal impact of X on Y:
