Measuring evidence for mediation in the presence of measurement error

Mediation analysis empirically investigates the process underlying the effect of anexperimental manipulation on a dependent variable of interest. In the simplestmediation setting, the experimental treatment can affect the dependent variablethrough the mediator (indirect effect) and/or directly (direct effect). However,what appears to be an indirect effect in standard mediation analysis may reflect adata generating processwithoutmediation, including the possibility of a reversedcausal ordering of measured variables, regardless of the statistical properties of theestimate. To overcome this indeterminacy where possible, we develop the insightthat a statistically reliabletotaleffect combined with strong evidence for conditionalindependence of treatment and outcome given the mediator is unequivocal evidencefor mediation as the underlying causal model into an operational procedure. This isparticularly helpful when theory is insufficient to definitely causally order measuredvariables, or when the dependent variable is measured before what is believed tobe the mediator. Our procedure combines Bayes factors as principled measures ofthe degree of support for conditional independence, with latent variable modelingto account for measurement error and discretization in a fully Bayesian framework.Re-analyzing a set of published mediation studies, we illustrate how our approachfacilitates stronger conclusions.