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I am trying to figure out how to interpret the WAIC value computed based on two different Bayesian models. Is the value only used for comparing the models, such that the predictive capabilities of the model with a higher WAIC value is superior? Or does the value in itself say anything?

I have looked at BDA by Gelman and A student's guide by Lambert, but I still do not really get it.

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    $\begingroup$ Btw, a lower WAIC value indicates better model fit, not higher. $\endgroup$
    – Earlien
    Commented Jul 11, 2020 at 23:32

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The value by itself isn’t interpretable. It could be close to zero, greater than a million, or even negative. It is only useful for comparing models. Note that your models must be fit to the same data though in order to compare WAIC values.

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  • $\begingroup$ Thank you! That makes sense when you look at the formula for computing it. Do you know how much difference between the two modeled would be considered significant? $\endgroup$
    – MarG
    Commented Jul 12, 2020 at 5:49
  • $\begingroup$ In the past, I've used the same rule of thumb as suggested by Spiegelhalter for DIC: within 2 units is considered about the same, within 7 units similar model fit, and >7 different. I haven't seen anyone use different guidelines. $\endgroup$
    – Earlien
    Commented Jul 12, 2020 at 7:19
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    $\begingroup$ By the way. if you do get a negative WAIC value, it generally means the plug-in estimate isn't a good representation of your posterior. Try another variant of WAIC (similarly for DIC). Some variants here: stats.stackexchange.com/questions/331928/dic-waic-in-jags/… $\endgroup$
    – Earlien
    Commented Feb 8, 2021 at 0:43

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