Measuring Evidence for Mediation in the Presence of Measurement Error

Mediation analysis empirically investigates the process underlying the effect of an experimentalmanipulation on a dependent variable of interest. In the simplest mediation setting, theexperimental treatment can affect the dependent variable through the mediator (indirecteffect) and/or directly (direct effect). Recent methodological advances made in the field ofmediation analysis aim at developing statistically reliable estimates of the indirect effectof the treatment on the outcome. However, what appears to be an indirect effect throughthe mediator may reflect a data generating process without mediation, regardless of thestatistical properties of the estimate. To overcome this indeterminacy where possible,we develop the insight that a statistically reliable indirect effect combined with strongevidence for conditional independence of treatment and outcome given the mediator isunequivocal evidence for mediation (as the underlying causal model generating the data)into an operational procedure. Our procedure combines Bayes factors as principled measuresof the degree of support for conditional independence, i.e., the degree of support for a Nullhypothesis, with latent variable modeling to account for measurement error and discretizationin a fully Bayesian framework. We illustrate how our approach facilitates stronger conclusionsby re-analzing a set of published mediation studies