Physical Sciences and Mathematics Commons^™

A Unification Of Mediation And Interaction: A Four-Way Decomposition, Tyler J. Vanderweele

Harvard University Biostatistics Working Paper Series

It is shown that the overall effect of an exposure on an outcome, in the presence of a mediator with which the exposure may interact, can be decomposed into four components: (i) the effect of the exposure in the absence of the mediator, (ii) the interactive effect when the mediator is left to what it would be in the absence of exposure, (iii) a mediated interaction, and (iv) a pure mediated effect. These four components, respectively, correspond to the portion of the effect that is due to neither mediation nor interaction, to just interaction (but not mediation), to both mediation …