Treatment interactions can be hard to estimate from data.

Brendan Nyhan writes:

Per #3 here, just want to make sure you saw the Coppock Leeper Mullinix paper indicating treatment effect heterogeneity is rare.

My reply:

I guess it depends on what is being studied. In the world of evolutionary psychology etc., interactions are typically claimed to be larger than main effects (for example, that claim about fat arms and redistribution). It is possible that in the real world, interactions are not so large.

To step back a moment, I don’t think it’s quite right to say that treatment effect heterogeneity is “rare.” All treatment effects vary. So the question is not, Is there treatment effect heterogeneity?, but rather, How large is treatment effect heterogeneity? In practice, heterogeneity can be hard to estimate, so all we can say is that, whatever variation there is in the treatment effects, we can’t estimated it well from the data alone.

In real life, when people design treatments, they need to figure out all sorts of details. Presumably the details matter. These details are treatment interactions, and they’re typically designed entirely qualitatively, which makes sense given the difficulty of estimating their effects from data.

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