Loo to compare ordered vs continuous response models

I’m aware that loo/waic require that model outcome variables are the same, but wonder if LOO can be used when a different link is applied to the same response variable? For example;

m1 <- brm(ordered(y) ~ …, family=cumulative())
m2 <- brm(y ~ …)

LOO(m1,m2, resp=“y”)

Currently this prints the warning “Model comparisons are likely invalid as the response values of at least two models do not match.”

If loo is not suitable here, is there a way to compare these models, or is the selection of the link conceptually prior to the running of the model in some way?

LOO shouldn’t be used to compare continuous and discrete models even if “y” was the same.


You can do the comparison only if you compute from the continuous predictive distribution the probabilities of intervals that can be considered to match the discrete values. It is better to use discrete distribution from the beginning for discrete outcomes.