Prior Predictive Checks for the Method of Covariances in Bayesian Mediation Analysis

Bayesian mediation analysis using the method of covariances requires specifying a prior for the covariance matrix of the independent variable, mediator, and outcome. Using a conjugate inverse-Wishart prior has been the norm, even though this choice assumes equal levels of informativeness for all elements in the covariance matrix. This paper describes separation strategy priors for the single mediator model, develops a Prior Predictive Check (PrPC) for inverse-Wishart and separation strategy priors, and implements the PrPC in a Shiny app. An empirical example illustrates the possibilities in the app. Guidelines are provided for selecting the optimal prior specification for the prior knowledge researchers wish to encode.