Imagine I am trying to fit a multilevel model on products, and want to group by product type.
In cases where product types have all the same predictors this is straight-forward. E.g. you might estimate the effect of color on sales or something similar.
But what if some predictors only make sense for some of the product types? Like a "leg length" feature might make sense for shorts if people have preference for how far above or below the knee they like their shorts, but not for pants which are always full length. And it may make yet less sense for shirts, since the do not at all have a leg length.
In that case, is there a way to handle that or is it best to have different models per group? For the features that are shared and are expected to be drawn from the same distribution, I guess we lose some benefit there, so that’s why I’m wondering if the models can be done as a single model.
I’ve thought about a number of things (e.g. for products that don’t have the feature, setting it to a constant value, or to a random value drawn from a distribution of feature values from products where the feature does make sense, etc) but all seem to have very obvious problems.