This is a statistical question, but more of a meta-statistical question. However, it's not a meta-discussion question, so I hope this is the correct venue.
I'm asking this because maybe I'm just not understanding something. I recently did a mixed-level GLM to investigate potential effects of a binary predictor on a continuous metric, over several years, for several locations. I set up a two-way interaction model with random intercepts and slopes per location. A classic repeat-measures mixed-level model.
Someone pipes up that such a model merely showed "correlation" and not "causation" and said that the question would only be worth looking at with a differences-of-differences (DID) model. Basically a "come back when you're ready to play" response.
Here's the thing that's got my head scratching. A DID is essentially a type of regression model, where "event" and "time" are binary coded and used as predictors (with interaction) vs. a response variable. Am I right? The basic DID also doesn't have compensation for autocorrelation.
I'm scratching my head, because I don't see how DID shows causation vs. correlation any more than any other type of model.
Am I just somehow not seeing something very obvious?