Thanks your answer was very complete! Especially the second point is important to me.
What about WAIC/DIC in presence of random effects such as in the Conditional Autoregressive (CAR) model? If I compute the DIC/WAIC on i) a model with just the random effect variables and ii) a model with random effects AND covariates, I always get lower or equal DIC/WAIC for the former.
How do you interpret these results? I think the random effects get confusion on the metrics, don’t they? Do you have any experience on this?
I ask this because this is one of my source of confusion about the evaluations.