I’m stuck on how to specify a model—or if I can—and thought some of you might have ideas.

Imagine you have a continuous response variable Y that is influenced by two continuous properties A and B. What I want to quantify is the effect of A on Y independent of B. Simple enough. Where this gets tricky is with the data.

The data come from an experiment where there’s a categorical treatment X. What we observe is the response of Y to X and the response of A to X (but B is not measured). If I were to just regress Y against A I would have an endogeneity issue since the variation of each is due to the same manipulation. Is there any way around this (without some kind of instrument)? Could I regress Y against the treatment X and then use a hyperparameter where the effect of X on Y is somehow a function of A?