Comparing the Accuracy of Three Predictive Information Criteria for Bayesian Linear Multilevel Model Selection

Bayesian multilevel modeling techniques have become increasingly popular. As researchers leverage these techniques, information criteria—fit indices which provide information about a model’s fit to the data—play an important role in disambiguating between competing models. The deviance information criteria (DIC) has been historically popular and is computationally easy, yet newer indices such as Watanabe-Akaike information criterion (WAIC) and an approximation to the leave-one-out cross-validation information criterion (LOO-CV) have been recently introduced. However, researchers may be unsure about which criteria to use, as to our knowledge, a systematic evaluation of these Bayesian criteria in a multilevel context has not yet been undertaken. Complicating this matter, computation of these indices using the so-called marginal likelihood is sometimes recommended, yet use of the conditional likelihood is easier and more readily found in some popular software. In addition, researchers frequently select the model with the lowest value of the information criteria, discounting the presence of uncertainty in calculating the criteria. Across two extensive simulation studies meant to mimic experimental and observational studies, we investigate the model selection accuracy of conditional and marginal versions of DIC, WAIC, and LOO-CV; we also compare a lowest wins strategy versus one that considers model selection uncertainty. In general, indices based on the marginal likelihood had a slight advantage and performed similarly to each other, whereas under the conditional likelihood WAIC and LOO-CV outperformed DIC. In addition, we argue that a selection strategy that simply chooses the model with the lowest information criteria may result in overfitting.