Measuring Evidence for Mediation in the Presence of Measurement Error
2020
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). Recent methodological advances made in the field of
mediation analysis aim at developing statistically reliable estimates of the indirect effect
of the treatment on the outcome. However, what appears to be an indirect effect through
the mediator may reflect a data generating process without mediation, regardless of the
statistical properties of the estimate. To overcome this indeterminacy where possible,
we develop the insight that a statistically reliable indirect 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 generating the data)
into an operational procedure. Our procedure combines Bayes factors as principled measures
of the degree of support for conditional independence, i.e., the degree of support for a Null
hypothesis, with latent variable modeling to account for measurement error and discretization
in a fully Bayesian framework. We illustrate how our approach facilitates stronger conclusions
by re-analzing a set of published mediation studies.
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