Path-Free Decomposition for Direct, Indirect and Interaction Effects in Mediation Analysis

Abstract: Given a binary treatment and a binary mediator, mediation analysis decomposes the total effect of the treatment on an outcome variable into direct and indirect effects. However, the existing decompositions are "path-dependent", and consequently, there appeared different versions of direct and indirect effects. Differently from these, this paper proposes a "path-free" decomposition of the total effect into three sub-effects: direct, indirect, and treatment-mediator interaction effects. Whereas the interaction effect has been part of the indirect effect in the existing two-effect decompositions, it is separately identified in our three-effect decomposition. All effects are found using conditional means, but not conditional densities, and are estimated with ordinary least squares estimators. Simulation and empirical analyses are provided as well.