Variable Selection for Mediators under a Bayesian Mediation Model

This study proposes a Bayesian variable selection approach to select mediators and quantify their respective posterior probabilities in exploratory mediation analysis. Monte Carlo simulation studies demonstrate that the proposed method has high statistical power in selecting mediating effects and low Type I error rate in excluding null effects. By estimating the probability of a given mediating effect via the posterior distribution, the proposed method quantifies the variable's influence on a continuum scale. This is an attractive and unique gain that neither conventional p-value-based mediation methods nor the regularization-based LASSO method for exploratory mediation possess. We offer four decision rules to assist in selecting mediators and excluding null effects to minimize a common problem (i.e., elevated type I errors) in the exploratory context, as well as provide an empirical example to illustrate the proposed method's application and interpretation. We end with a discussion of the work and directions for future work.