There has been a good amount of discussion recently between those who prefer the potential outcomes approach and those who prefer the causal diagram/do-calculus approach. Since a letter I wrote has been used as an example in this discussion, I thought I'd add my two cents. 1/n
First, it is worth noting that these two approaches are both ingenious ways to add methods for causal inference into our toolbox. They also happen to be very similar, and (usually) lead to the same results. 2/n
In the potential outcomes approach, we define new variables, such as Y(x), which can be interpreted as "the value Y would potentially have if, possibly counter to fact, X took value x." These variables can then be fed through our usual statistical tools. 3/n
In the do-calculus approach, we do not introduce any new variables. Instead, we introduce a new operator, the do-operator. We may then be interested in something like E[Y|do(x)], which is the expected value of Y if we set X to value x. 4/n
The next challenge is to map what we want to know into expressions involving things we actually know and observe in the world. In the do-calculus approach, we can construct a causal diagram that depicts known causal relations between observable variables. 5/n
Once the causal diagram is constructed, we can apply a set of rules, the do-calculus, to map expressions such as E[Y|do(x)] into expressions that do not include the do-operator. 6/n
With potential outcomes, we rely on certain identification conditions to make the connection to our observed data. These include consistency, conditional exchangeability + positivity, etc. 7/n
Each of these conditions can be expressed using our existing statistical tools and notation. The downside is that we need to somehow map our knowledge of things that we see (observed variables) to things we don't see (potential outcomes). 8/n
Single world intervention graphs (SWIGs) were designed to aid us in translating our knowledge of the observable to the unobservable. Starting with a causal diagram, we can make a few modifications and end up with our SWIG, which actually has the potential outcomes on it. 9/n
From here, we can immediately read off the conditional independencies (including those for unobservable potential outcomes) implied by our knowledge of the observed world. SWIGs thus help us overcome one of the main limitations of the potential outcomes approach. 10/n
So which is to be preferred? Though I appreciate both approaches, for me, given my background in probability and statistics, I tend to feel more comfortable with potential outcomes, since I can use the machinery I am most familiar with. 11/n
But I can understand the viewpoint of people who prefer the do-calculus approach, since it doesn't introduce new unobservable variables. It is easy to construct examples where one approach may seem easier than the other. 12/n
As a final note, I need to mention that causal diagrams, as formalized by Pearl and colleagues, encode more assumptions than SWIGs. In particular, they encode 'cross-world' independence assumptions. 13/n
These assumptions apply to potential outcomes under different levels of X. There are real implications of these assumptions. For instance, they are needed for certain path-specific effects to be identifiable. 14/n
I'd like to finish with three conditional polls (let's see if this works!). First, which causal framework are you most comfortable with? 15/n
If you said potential outcomes, what field are you in? 16/n
If you said DAGS/do-calculus, what field are you in? 17/n
If you said other, please let me know what framework that is, and what field you are in! 18/n
