Practical implications of many high-Pareto K observations loo

Without seeing additional diagnostics (like LOO-PIT) it’s difficult to be certain, but this is the likely reason. You could compare which observations get high Pareto-k and if they all are observations that are the only observation for some species, then that would give additional support to this hypothesis.

If the high Pareto-k’s are only for the those observations that are the only one in some group, and we assume there is no model misspecification, then the posterior is still valid. Yes, the group effects for the groups having just one observation are probably unreliable, but that should show also in the width of the posterior for those effects. We can also say that the population prior is not very informative (they rarely are), and thus even with one observation in the group the prior and posterior for the group effect are quite different, Additional data may then change the posterior a lot, but not necessarily in a way that would be surprising given the current width of the posterior. Are you comparing this model with some other model?

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