I have some questions about LOOIC:

Can LOOIC be used to compare models with the SAME likelihood but DIFFERENT priors? (assuming all of the paretok diagnostics are fine etc?)

Can the LOOIC be used to compare models with a DIFFERENT likelihood / parameterisation, and also DIFFERENT priors? (i’m pretty sure this is a “yes” as otherwise surely LOOIC would not be very useful?!)
Also, I have the same questions but for the DIC.
 Yes, but do not use LOOIC to select your priors. In particular, LOOIC will prefer priors that are tightly concentrated around the point estimates that yield the best leaveoneout performance. There is no guarantee that the point estimates that yield maximal LOO performance are actually (very close to) the true parameter values.
 Yes.
For DIC we’ll have to let somebody else chime in, but I’m pretty confident the general attitude of this forum will be that you should prefer LOOIC to DIC anyway.
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See Crossvalidation FAQ questions 13, 22, and 23.
But also when using LOO, there is no sense in multiplying by 2 (there can be sense in multiplying by 1). CVFAQ 23.
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