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I am creating a Bayesian spatiotemporal model with the four type Knorr Held interaction proposal. I am trying the different type of interactions and I want to select the best model based on DIC, WAIC and CPO.

The problem I have is that the DIC and WAIC values suggest to select the model with interaction type III while CPO suggests to select interaction type IV. Which metric prevails when they don't agree?

Thanks in advance

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