In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). A multilevel mediation model is used as an illustrative example to compare different types of DIC and WAIC. More specifically, the study compares the performance of conditional and marginal DICs and WAICs, and investigates their performance with missing data. The study focuses on two versions of DIC (DIC[subscript 1] and DIC[subscript 2]) and one version of W AIC. In addition, the study explores whether it is necessary to include the nuisance models of incomplete exogenous variables in likelihood. Based on the simulation results, whether DIC[subscript 2] is better than DIC[subscript 1] and WAIC and whether including the nuisance models of exogenous variables in likelihood functions depends on whether using marginal or conditional likelihoods. Overall, the marginal likelihood based DIC[subscript 2] that excludes the likelihood of covariate models generally had the highest true model selection rates. [This paper will be published in "Behavior Research Methods."]