Bayesian model selection for multilevel mediation models

Mediation analysis is often used to explore the complex relationship between two variables through a third mediating variable. This paper aims to illustrate the performance of the deviance information criterion, the pseudo-Bayes factor, and the Watanabe-Akaike information criterion in selecting the appropriate multilevel mediation model. Our focus will be on comparing the conditional criteria (given random effects) versus the marginal criteria (averaged over random effects) in this respect. Most of the previous work on the multilevel mediation models fails to report the poor behavior of the conditional criteria. We demonstrate here the superiority of the marginal version of the selection criteria over their conditional counterpart in the mediated longitudinal settings through simulation studies and via an application to data from the Longitudinal Aging Study of the Amsterdam study. In addition, we demonstrate the usefulness of our self-written R function for multilevel mediation models.