Comparing a hurdle lognormal model to a gaussian model with loo-cv

Modeling
1

I have been posting a lot lately about comparing models with different link functions fit to the same data (see here and here). This post is an extension of those.

I am simply wondering if I can compare a hurdle lognormal model to a gaussian model using the same procedure as if I were comparing a gamma to a gaussian?

From what I understand (based on this post by Andrew Heiss the hurdle works by decomposing the model into two processes, one Bernoulli-type process for the zero vs non-zero and a lognormal for the non-zero. The gaussian of course does not contain the Bernoulli process.

I have conducted a hurdle lognormal and gaussian regression performed on the same data, loo’d each, and then compared them via loo_compare(huLogNorm_model, gaussian_model) which yielded an output with no warning messages.

My question is, assuming all relevant diagnostics are ok in both models, can I trust the output of this loo comparison? It looks like, from this post that I can, but I just want to make sure.

2

Since one the models is combination of discrete and continuous and other one is continuous, you need to do the model comparison in discrete space by completely discretizing both models. Nabiximols case study explains why for integer valued targets the discretization is super easy. Chapter 23 of Bayesian Workflow book has more discussion on discretization for loo-cv

3

Thanks so much @avehtari. I will consult the case study.