As a criterion for model fit and model comparison, the DIC can be retrieved using an R-function in the bayzRfunc.R file (see Using R and R Coda for loading the bayzRfunc.R functions). The DIC is not (yet) available for output from discrete trait (threshold) models.
The 'best' model as indicated by the DIC is simply the one with lowest DIC, irrespective of the number of parameters. The DIC is comparable to the AIC (Aikaikes Information Criterion) in that there is already a penalty included for number of parameters fitted, and it is possible that larger, more complex, models show worse (higher) DIC. This would reflect that the more complex model does not improve the fit sufficiently in order to support estimating the additional parameters. Like AIC, DIC also allows to select a 'best' model for non-nested models.
There are two DIC functions supplied in the bayzRfunc.R package: