Different Roles of Prior Distributions in the Single Mediator Model with Latent Variables.

In manifest variable models, Bayesian methods for mediation analysis can have better statistical properties than commonly used frequentist methods. However, with latent variables, Bayesian mediation analysis with diffuse priors can yield worse statistical properties than frequentist methods, and no study to date has evaluated the impact of informative priors on statistical properties of point and interval summaries of the mediated effect. This article describes the first examination of using fully conjugate and informative (accurate and inaccurate) priors in Bayesian mediation analysis with latent variables. Results suggest that fully conjugate priors and informative priors with the same relative prior sample sizes have notably different effects at  = 200 and 400, than at  = 50 and 100. Consequences of a small amount of inaccuracy in priors for loadings can be alleviated by making the prior less informative, whereas the same is not always true of inaccuracy in priors for structural paths. Finally, the consequences of using informative priors depend on the inferential goals of the analysis: inaccurate priors are more detrimental for accurately estimating the mediated effect than for evaluating whether the mediated effect is nonzero. Recommendations are provided about when to gainfully employ Bayesian mediation analysis with latent variables.