What is “explanation”?

“Explanation” is this thing that social scientists (or people in their everyday lives, acting like social scientists) do, where some event X happens and we supply a coherent story that concludes with X. Sometimes we speak of an event as “overdetermined,” when we can think of many plausible stories that all lead to X.

My question today is: what is explanation, in a statistical sense?

To understand why this is a question worth asking at all, compare to prediction. Prediction is another thing that we all to, typically in a qualitative fashion: I think she’s gonna win this struggle, I think he’s probably gonna look for a new job, etc. It’s pretty clear how to map everyday prediction into a statistical framework, and we can think of informal qualitative predictions as approximations to the predictions that could be made by a statistical model (as in the classic work of Meehl and others on clinical vs. statistical prediction).

Fitting “explanation” into a statistical framework is more of a challenge.

I was thinking about this the other day after reading a blog exchange that began with a post by sociologist Fabio Rojas entitled “the argo win easily explained”:

The Academy loves well crafted films that are about actors or acting, especially when actors save the day. These films often beat other films. Example: Shakespeare in Love beats Saving Private Ryan; the Kings Speech beats Black Swan, Inception and Social Network. Bonus: Argo had old Hollywood guys saving the day.

Thomas Basbøll commented, skeptically:

If is is so easy to explain, why didn’t you predict it, Fabio? . . . It’s not like you learned anything new about the nominated films over the past 48 hours besides who actually won. Isn’t this just typical of sociological so-called explanations? Once something had happened, a sociologist can “easily” explain it. If Lincoln had won I suppose that, too, would have been a no-brainer for sociology.

I could see where Basbøll was coming from, but his comment seemed to strong to me, so I responded to the thread:

To be fair, Fabio didn’t say “the argo win easily predicted,” he said “explained.” That’s different. For a social scientist to make a prediction is clear enough, but we also spend a lot of time explaining. (For example, after the 2010 congressional elections, I posted “2010: What happened?”.) Explanation is not the same as prediction but it’s not nothing. For a famous example, Freudian theory explains a lot but does not often predict, and Freudianism has lots of problems, but it is not an empty theory. The fact that Fabio could’ve explained a Lincoln win does not make his Argo explanation empty.

But this got me thinking: what exactly is explanation, from a statistical standpoint? (Over the years I’ve spent a lot of time considering commonsense “practical” ideas such as mixing of Markov chains, checking of model fit, statistical graphics, boundary-avoiding estimates, and storytelling, and placing them in a formal statistical-modeling framework. So I’m used to thinking this way.) Explanation is not prediction (for the reason indicated by Basbøll above), but it’s something.

I think that “explanation,” even in the absence of “prediction,” can be useful in helping us better understand our models. Rojas’s Argo explanation helps him elaborate his implicit theory of the Oscars, essentially constraining his theory as compared to where it was before the awards were announced. In that sense, “explanation” is an approximation to Bayesian updating. What “explanation” does is to align the theory to fit the data, which is comparable to the statistical procedure of restricting the parameters to the zone of high likelihood for the observed data.

Prediction is important, it’s essential for model checking, but explaining is another word for inference within a model. Without explanations (including after-the-fact explanations), it would be difficult to understand a model well enough to use it. Another way of putting it is that explanation is a form of consistency check.

What would make all my theorizing relevant here? It would be relevant to social science if it helps us to formulate our explanations in terms of what we have learned from the data: in this case, how are Rojas’s post-Oscars views of the world different from his views last week. If Basbøll is right and Rojas did not forecast the Argo win ahead of time, that’s fine; to that extent, his explanation will be more valuable to the extent that it articulates (even if only qualitatively) the role of the new information in refining his theories.

I’m curious what Rojas thinks of this, as he’s the one who created that particular explanation. I am sympathetic with Basbøll’s skepticism, but I feel like I get some value from explanations such as Rojas’s (or Freud’s), so I’d like to adapt my philosophy of scientific understanding to allow a role for such explanations, rather than to follow a Popper-like route and dismiss them as meaningless. Much of my efforts as a statistician have been devoted to adjusting the foundations to give a place for methods that are evidently (to me) helpful in understanding the world.

P.S. Larry and others note that to really be an “explanation,” a story should be causal. That sounds right to me. A purely predictive explanation would not really feel like an explanation at all. This is an important point that I’d not thought of, when writing the blog above.