Crude measurements and interactions

[Guest]

Hello statalist

This is more of a statistics question than specific stata related question.

If am wondering if when you are studying a model with an interaction term (So X affects Y, but the effect of X on Y is conditioned by Z), could the lack of a statistical significant interaction term both be due to a crude measurement of the primary variable (X) or can it only be due to the moderator (Z).

Mathematically i would assume that it could be due to X and Z, but i am not completely sure.

I hope someone more knowledgeable than me can help.

Kind regards Guest

[Mike Lacy]

On general principles, I'd point out that any measurement problem in any variable in a statistical model will reduce the capacity to detect the true effect. I'd also respond more specifically to your thinking of a "primary" variable and a "moderator" variable as distinct and different things. While this is presumably a conceptually correct way to think about your problem in its context, there is no statistical difference between the two. They are each simply components of a product variable, X*Z, that appears in the design matrix, and the analytic machinery (e.g., -regress- or -anova-) doesn't know the difference between them, and would respond the same to problems in either variable.