Power in Bayesian Mediation Analysis for Small Sample Research

Abstract

Bayesian methods have the potential for increasing power in mediation analysis (Koopman, Howe, Hollenbeck, & Sin, 2015; Yuan & MacKinnon, 2009). This article compares the power of Bayesian credibility intervals for the mediated effect to the power of normal theory, distribution of the product, percentile, and bias-corrected bootstrap confidence intervals at N ≤ 200. Bayesian methods with diffuse priors have power comparable to the distribution of the product and bootstrap methods, and Bayesian methods with informative priors had the most power. Varying degrees of precision of prior distributions were also examined. Increased precision led to greater power only when N ≥ 100 and the effects were small, N < 60 and the effects were large, and N < 200 and the effects were medium. An empirical example from psychology illustrated a Bayesian analysis of the single mediator model from prior selection to interpreting results.

Keywords:

• Bayesian statistics
• power
• single mediator model
• small sample sizes

ACKNOWLEDGMENTS

The authors would like to thank Stephen G. West and Craig K. Enders for their feedback during the development of the research presented in this article.

FUNDING

This research was supported in part by the National Institute on Drug Abuse, Grant No. R37DA009757.

Additional information

Funding

This research was supported in part by the National Institute on Drug Abuse, Grant No. R37DA009757.