I estimate model parameters for 2 glmm models using MCMC in R2JAGS. I then use DIC to assess the relative fit of the models:
Model 1 y~ site + treatment (DIC = 922.1)
Model 2 y~ site (DIC = 921.8)
Given the low Δ DIC between models 1 and 2, I understand there is no improvement to the model if the term 'treatment' is added. However, when I look at the parameter estimates for model 1, the credible interval for the 'treatment' term does not contain '0', indicating it is an important variable.
If 'treatment' is an important variable from the MCMC, why does the model fit from the DIC not change when 'treatment' is dropped? Which is the preferred model in this situation?
