Comparing DIC and WAIC for multilevel models with missing data

Area of Science:

• Bayesian statistics
• Statistical modeling

Background:

• Deviance Information Criterion (DIC) and Watanabe-Aike Information Criterion (WAIC) are key Bayesian model assessment tools.
• Comparing different versions of DIC and WAIC is crucial for accurate statistical inference.

Purpose of the Study:

• To compare the performance of conditional and marginal DIC and WAIC.
• To investigate the impact of missing data on these criteria.
• To evaluate the necessity of including nuisance models for incomplete exogenous variables.

Main Methods:

• Utilized a multilevel mediation model for comparative analysis.
• Focused on two versions of DIC ($$, $$) and one version of WAIC.
• Simulated data to assess performance under various conditions, including missing data.

Main Results:

• The performance comparison between $$, $$, and WAIC depended on the use of marginal or conditional likelihoods.
• Including nuisance models for exogenous variables was contingent on the likelihood type.
• Marginal likelihood-based $$, excluding covariate models, demonstrated superior true model selection rates.

Conclusions:

• Marginal likelihood-based $$ is a robust criterion for Bayesian model selection, particularly with missing data.
• The choice between conditional and marginal approaches impacts the effectiveness of DIC and WAIC.
• Excluding covariate models in marginal likelihood calculations can enhance model selection accuracy.