Reply to commentary by Imai, Keele, Tingley, and Yamamoto concerning causal mediation analysis

Abstract

This comment clarifies how structural causal models unify the graphical and potential outcome approaches to mediation, and why the resulting mediation formulas are identical in both frameworks. It further explains under what conditions ignorability-based assumptions are over-restrictive and why such assumptions require graphical interpretations before they can be judged for plausibility. Finally, the comment explains the key difference between traditional and modern methods of causal mediation, and demonstrates why the notion of mediation requires counterfactual rather than Bayes conditionals to be properly defined.