Jacob Felson writes:
Say we have a statistically significant interaction in non-experimental data between two continuous predictors, X and Z and it is unclear which variable is primarily a cause and which variable is primarily a moderator. One person might find it more plausible to think of X as a cause and Z as a moderator and another person may think the reverse more plausible. My question then is whether there is are any set of rules or heuristics you could recommend to help adjudicate between alternate perspectives on such an interaction term.
I think in this setting, it would make sense to think about different interventions, some of which affect X, others of which affect Z, others of which affect both, and go from there. Rather than trying to isolate a single causal path, consider different cases of forward casual inference. My guess is that the different stories regarding moderators etc. could motivate different thought experiments (and, ultimately, different observational studies) regarding different potential interventions.
So I would not try to “adjudicate” between different stories; rather, I’d recognize that they could all be appropriate, just corresponding to different interventions. Also, all the above would hold even if there are only main effects, no interactions needed. And, for that matter, statistical significance would not be needed either for you to look at these questions.