Variable Selection for Mediators under a Bayesian Mediation Model

Abstract

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.

Keywords:

• Bayesian variable selection
• decision rules
• exploratory mediation analysis
• Gibbs sampling
• model uncertainty

Acknowledgements

Dr. Dingjing Shi gratefully acknowledges the support of the Office of the Vice President for Research and Partnerships from the University of Oklahoma through the Junior Faculty Fellowship, which was instrumental in carrying out the research presented in this paper.

Dr. Amanda J. Fairchild would like to gratefully acknowledge the sabbatical leave granted to her by the University of South Carolina, which provided the time to help make this research possible.

We are grateful to the editor, Dr. George A. Marcoulides, and the anonymous reviewers for their careful reviews and insightful comments that greatly improved the manuscript.

Notes

1 There are methods to handle models with categorical outcomes and/or mediators, but those aren’t discussed here.