Mediation Analysis in Bayesian Extended Redundancy Analysis with Mixed Outcome Variables

Extended redundancy analysis (ERA) is a statistical approach to component-based multivariate regression modeling that explores interrelationships among multiple sets of while incorporating regression with a data-reduction technique.The extantmodels that utilize ERA have assumed the outcome variables with the same data type. Also, ERAmodels focused on estimating direct pathways only without explicitly addressing mediation effects. In this paper, ERA is extended to handlemultiplemediators and mixed types of outcome variables by adopting a Bayesian framework, taking into account correlation structure among all of the outcome variables.Theproposed method develops an algorithmthat derives the joint posterior distribution of parameters using a Markov chain Monte Carlo algorithm. Simulations and an empirical dataset are provided to illustrate the usefulness of the proposed method.