I am here to ask you for bits of advice on a problem I’d try to formalize and then translate into Stan.

Let’s say I have Y \in \mathbb{R^N} measures of a phenomenon that I formerly treated as a straightforward regression -no mixed effects- using D covariates (including the intercept) :

Now, I would like to extend my model knowing that the values of Y depend on D_1 covariates that can be grouped under a *biotic* effect and another group of D_2 covariates that are an *abiotic* effect so that D = D_1 + D_2.

I would like to compute the relative magnitude \alpha of the two groups of covariates, i.e. if the abiotic component is more important than the biotic one.

So, firstly I proposed to extend the model as:

Then, thanks to the former mathematical formalization, I now think that a better approach should be using a finite mixture of 2 components, modelling the \mu with the the covariates.

Do you think that I am unnecessarily complicating my life and there are simpler approaches? Am I catching a red herring?