I’m not sure if this title is fitting but I don’t know how else to concisely describe the issue. I’m using Bambi but I guess that’s not really relevant here.
I have a model with a continuous outcome y and two categorical input variables x1 and x2. x1 has two categories, a and b, and x2 also has two categories, 0 and 1. I want to model an interaction effect between x1 and x2.
So the model formula would be
y ~ x1 + x2:x1
The problem is that all data points in category a of variable x1 have a 0 value in variable x2. For category b there are both 0 and 1 values. I am not interested in getting an estimate for the x2 parameter in the case of x1=a, but in theory these data could exist. I started out with a hierarchical model:
y ~ x1 + x2|x1
which kinda worked, the problem is that I’m getting very wide HDIs for both the x1 and the x2 parameter in the case of x1=a (I don’t really care about the x2 parameter here though). So the next thing I did was using the first formula and setting a very narrow prior for x2 when x1=a and a flatter prior for x2 when x1=b. This seemed to have worked, i.e. the x1 parameter for when x1=a does not have a huge HDI anymore, but I’m wondering if this is a legitimate approach or if there’s a better way to deal with such a situation?
Hope things are clear, let me know if not. Thanks!