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.