I want to model and predict a variable y which is the product of two components a discrete variable f which has a Poission distribution and s which has a positive continuous distribution. For instance if f is 0 then y is also 0. I also have some covariates x that drive f and s.
y = f * s
If I just model y directly as continuous, I don’t have componding errors but my model might also be a bit weak as it doesn’t understand the underlying semi discrete nature.
If I just model f and s, then y might be also inaccurate.
Does it make sense to have 3 likelihood equations in my model, for (f, s, y)?