JAGS allows reporting of DIC and also PED (penalized expected deviance). What are differences between these two statistics? Which is better for what purpose? DIC was the first one, PED was evidently added later, so what was the reason for introducing PED? In what regard and in which situations/type of models is it more appropriate than DIC?
I did a little research and found an answer from Martyn Plummer (JAGS author) stating that the difference is in the penalty for complexity of the model. However, when I looked at my models, I noticed that even if I compare models with the same structure, just different covariate (but always the same dependent variable), I notice that although DIC and PED are correlated many times, there is still some variability and sometimes they both select a different models. And sometimes they are not even correlated:
Corresponding DIC and PED are always from one model run, so MCMC stochasticity cannot explain the variability. Model complexity is the same in all cases, as well as the response variable, the models only differ in the covariate used. Thus, Martin Plummers' answer doesn't explain it for me.
Subquestion: In AIC, if the difference of AIC between two models was greater than 2, we said that the models "differ enough". What would be the equivalent "rule of thumb" for DIC and PED? Is it still 2, or is it 1?
