Thanks for the answer!
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Pooling vs. no pooling
I agree. It’s just something that came up again and again when talking to psychiatry researchers. I have also had no-pooling models tested explicitly against multilevel ones and faring much worse, but still the critique came. But yes, posterior predictive checks by participants is something to work on. -
Extracting individual loo scores from multilevel model
I’d also be happy to hear more from @avehtari as to how the loo scores of individual participants in the multilevel model could be interpreted and what they could be used for. -
Mixture model
One of the models at stake is pretty hard to fit (divergences and chains stalling). After discussions here (e.g. [Clarification] Divergences during sample_prior = "only" model fitting) we managed to fit it with no divergences by using a simplex prior on the btw subject variance across parameters. Adding that model to a mixture model has so far just generated endless divergences. -
Qualitative model checking: yes! We had Danielle in Aarhus a couple of weeks ago (talk here: https://youtu.be/tNkmsAOn7aU) and I am converted :-)