A Tutorial in Bayesian Mediation Analysis With Latent Variables

Maximum Likelihood (ML) estimation is a common estimation method in Structural Equation Modeling (SEM), and parameters in such analyses are interpreted using frequentist terms and definition of probability. It is also possible, and sometimes more advantageous (Lee & Song, 2004: Rindskopf, 2012), to fit structural equation models in the Bayesian framework (Kaplan & Depaoli, 2012: Levy & Choi, 2013: Scheines, Hoijtink, & Boomsma, 1999). Bayesian mediation analysis has been described for manifest variable models (Enders, Fairchild, & MacKinnon, 2013; Yuan & MacKinnon, 2009). This tutorial outlines considerations in the analysis and interpretation of results for the single mediator model with latent variables. The reader is guided through model specification, estimation, and the interpretations of results obtained using two kinds of diffuse priors and one set of informative priors. Recommendations are made for applied researchers and annotated syntax is provided in R2OpenBUGS and Mplus. The target audience for this article are researchers wanting to learn how to fit the single mediator model as a Bayesian SEM.