causal inference

One area I’ve gotten interested in lately is causal inference. For those of you not familiar, it’s a methodology that attempts to find and validate cause-effect relationships between variables. The key is that it attempts to do so using data without having to rely on controlled experiments. (For an introduction for the casual reader, I highly recommend Judea Pearl’s book The Book of Why.)

One concept I found interesting was the implications of something called a collider. A collider is a variable that is the effect of two or more variables. As a simple example, consider the following:

The way to read this diagram is that fame is a function (or effect) of money, talent, and looks. In other words, fame = f(money, talent, looks). In this example, fame is a collider relative to money, looks, and talent because they all have arrows pointing into fame.

The interesting implication from the book is the following: given that you hold the level of a collider constant, the other variables become dependent upon each other even though there is no causal influence on them.

To understand this better, let’s use an even simpler example: X + Y = Z. In this case, Z is a function of X and Y (i.e. Z = f(X,Y)), so Z is a collider with respect to X and Y:

Here’s the key point: if we fix the value of Z at some specific value (say 10, so we’re left with the relationship X + Y = 10), then X and Y become correlated. In other words, if I know the value of X (say 8), then I can infer Y (i.e. 2).

The interesting finding from causal inference is that this dynamic generalizes. Said another way, for a given level of Z, information about X automatically gives me some information about Y, even if I can’t observe Y directly.

Almost Famous

Why is this interesting? Let’s go back to our fame example. Assuming our causal model is valid, then we can say that for a given level level of fame, if we know something about their level of wealth, we can infer something about their level of looks and talent. If we simplified it down for a minute to say just include looks and talent, then we could say – for a given level of fame – we’d expect that a person who is more attractive is likely to be less talented. (Another way to think about this is if they were both attractive and talented, they’d be even more famous).

I haven’t done an analysis to verify this yet, but it’d be interesting to run an experiment. For example, look on social media for actors who have a similar level of followers (as a proxy for fame). Within that cohort, if the model is valid then you would see a spectrum ranging from the good-looking-but-hacky to the talented-but-ugly.

Counterintuitive Hiring

This finding has interesting implications in many places. Take hiring, for example. Consider, for example, a hypothesis that seniority_level = f(skill, likability). If you think both skill and likability are positively correlated to seniority level, then – for a given level of seniority – consider that the most skilled person is likely to be the one you personally like the least.

These are of course toy examples; the causal structure of real life is likely to be much more complex. But they illustrate both the power of causal analysis and the sometimes counterintuitive truths behind the way the world works.