Some further thoughts on Causal Inference

So let me admit: Judea Pearl got under my skin reading the Book of Why. Not only negatively — I still don’t think he does justice to statisticians — but in the sense of saying that there is something important to think about.

I’m not sure that this had lead me in directions that bring me closer to Pearl, though. Some of my reaction is to say

Scientists (and statisticians) have had a habit of paying lip service to causal concerns (“This is an association, not causation”) but actually interpreting effects found through regression etc as, in fact, being causal; maybe we should be more careful about this.

I think of this realisation as being a bit like the way statistics has worked out that we’ve maybe been overly cavalier about data processing and exploration. Pearl doesn’t have much to say about demonstrating causal relations — he assumes you know them and just works with the consequences — but (and this may be the statistician in me) I rather feel that there is much more to do here than in the consequences of calling an effect causal. There’s lots of work being done right now, though (on both topics) so I’ll let that rest.

The thing that has niggled me is that the models that I think of as being justified are nothing like the toys that Pearl uses in his book. They’re based on physics or chemistry, or “first principles” understandings of biology or ecology along the lines of “predators eat prey”. And for these, I think I do know what causal relationships look like, even without Pearl — you read these off the model, or you make some change and simulate the model again. (Yes, that is the “do” operator, but what was needed was pretty obvious).

But is this very different from Pearl’s DAGs, except maybe in having more complex models? And it finally struck me that there is something that I think Pearl misses: time. One of the fundamental principles of our understanding of the world is a bar on backwards causation: causes happen along the direction of time. Now in most of Pearl’s examples (and in much of statistical causal inferences) time only appears implicitly: in a randomized controlled trial, one applies the treatment <i>then</i> measures the effect, similarly in Pearl’s models of Berkeley admissions. There is nothing in a DAG structure that requires that we satisfy the law of forward causation. I’m sure that the response would be

You do need to write down a model that corresponds to your causal understanding.

or more generally just that arrows in your DAG can only point forwards in time. Nonetheless, it does feel somewhat odd that the most fundamental properties of our understanding of cause and effect plays such as peripheral role in its mathematical description. I guess one might also view it as enforcing the “acyclic” part of DAGS. (Maybe it also says something about the nature of our understanding of causality.)

But this did get me to wondering about incorporating time explicitly into causal analysis. It’s certainly true that “arrows can only point forward in time” pretty much implies you have a DAG (I think that can be made formal). This also brings Pearls’ concepts closer to Granger causality. It both moves you closer to the sort of mechanistic models that I’m prepared to consider “causal” (at least outside randomized trials) and it would be interesting to see a Pearl-style approach to time-series models.