EXPRESS: Measuring Evidence for Mediation in the Presence of Measurement Error

Mediation analysis empirically investigates the process underlying the effect of an experimental manipulation on a dependent variable of interest. In the simplest mediation setting, the experimental treatment can affect the dependent variable through the mediator (indirect effect) and/or directly (direct effect). However, what appears to be an indirect effect in standard mediation analysis may reflect a data generating process without mediation, including the possibility of a reversed causal ordering of measured variables, regardless of the statistical properties of the estimate. To overcome this indeterminacy where possible, we develop the insight that a statistically reliable total effect combined with strong evidence for conditional independence of treatment and outcome given the mediator is unequivocal evidence for mediation as the underlying causal model into an operational procedure. This is particularly helpful when theory is insufficient to definitely causally order measured variables, or when the dependent variable is measured before what is believed to be the mediator. Our procedure combines Bayes factors as principled measures of the degree of support for conditional independence, with latent variable modeling to account for measurement error and discretization in a fully Bayesian framework. Re-analyzing a set of published mediation studies, we illustrate how our approach facilitates stronger conclusions.