Direct, indirect, and interaction effects based on principal stratification with a binary mediator

Given a binary treatment and a binary mediator, mediation analysis decomposes the total effect of the treatment on an outcome variable into various sub-effects, and there appeared two-, three-, and four-way decompositions in the literature. Using "principal stratification"based on the potential mediator types, we consider sub-treatment effects for "mediative never-takers, compliers, defiers, and always takers."In this approach, although it is difficult to pick any one decomposition over the others in general, a particular three-way decomposition becomes well suited, which is thus advocated to use. We present identification conditions for the effects using conditional means, which is then followed by simple estimators that are applicable to any outcome variable (binary, count, continuous, etc.). We also provide simulation and empirical studies.