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. 2009 Dec;14(4):301-22.
doi: 10.1037/a0016972.

Bayesian mediation analysis

Ying Yuan  1 , David P MacKinnon
Affiliations

Bayesian mediation analysis

Ying Yuan et al. Psychol Methods. 2009 Dec.

Abstract

In this article, we propose Bayesian analysis of mediation effects. Compared with conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian mediation analysis, inference is straightforward and exact, which makes it appealing for studies with small samples. Third, the Bayesian approach is conceptually simpler for multilevel mediation analysis. Simulation studies and analysis of 2 data sets are used to illustrate the proposed methods. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

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Figures

Figure 1
Figure 1
Diagram of the single-level mediation model.
Figure 2
Figure 2
Panel 1a–c show the prior, likelihood and posterior under weak prior information (µ ~ N(6, 1002)). In this case, the prior information has negligible effect on the posterior distribution. Panel 2a–c show the prior, likelihood and posterior under moderate prior information (µ ~ N(6, 62)). The posterior distribution is shrunk toward the prior distribution. Panel 3a–c show the prior, likelihood and posterior under strong prior information (µ ~ N(6, 22)). In this case, the prior information has strong effect on the posterior distribution. The likelihood is that x¯ ~ N(16, 42).
Figure 3
Figure 3
Informative normal prior distributions for α and β when the mediated effect size is zero, small, medium and large in the single level mediation simulation study.
Figure 4
Figure 4
Posterior distribution of the mediated effect (left panel) and the corresponding normal quantile-quantile plot (right panel) for the Bayesian single-level mediation analysis of the firefighter health promotion data.
Figure 5
Figure 5
Trace plot (a) and the Gelman-Rubin convergence statistic R (b) for posterior samples of the mediated effect αβ for the Bayesian single-level mediation analysis of the firefighter health promotion data.
Figure 6
Figure 6
Diagram of the two-level mediation model.
Figure 7
Figure 7
Trace plot of posterior samples of the indirect effect ab, total effect c and relative average indirect effect ab/c for the example of the multilevel mediation model.
Figure 8
Figure 8
The Gelman-Rubin convergence statistic R for the indirect effect ab, total effect c and relative average indirect effect ab/c in the example of the multilevel mediation model.
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