Measuring Evidence for Mediation in the Presence of Measurement Error

52 Pages Posted: 2 Jun 2020 Last revised: 29 Jul 2020

See all articles by Arash Laghaie

Arash Laghaie

Goethe University Frankfurt - Faculty of Economics and Business Administration

Thomas Otter

Goethe University Frankfurt - Department of Marketing

Date Written: May 5, 2020

Abstract

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 categorization
in a fully Bayesian framework. We illustrate how our approach facilitates stronger conclusions
by re-analzing a set of published mediation studies.

Keywords: mediation, causal model, identification, measurement, Bayes factor

JEL Classification: C11, C12, C52, M31

Suggested Citation

Laghaie, Arash and Otter, Thomas, Measuring Evidence for Mediation in the Presence of Measurement Error (May 5, 2020). Available at SSRN: https://ssrn.com/abstract=3593176 or http://dx.doi.org/10.2139/ssrn.3593176

Arash Laghaie

Goethe University Frankfurt - Faculty of Economics and Business Administration ( email )

Theodor-W.-Adorno-Platz 4
Frankfurt am Main, D-60323
Germany

Thomas Otter (Contact Author)

Goethe University Frankfurt - Department of Marketing ( email )

Frankfurt
Germany
++49.69.798.34646 (Phone)

HOME PAGE: http://www.marketing.uni-frankfurt.de/index.php?id=97?&L=1

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