Hi all,

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!