When studying effect heterogeneity between different subgroups (i.e., moderation), researchers are frequently interested in the mediation mechanisms underlying the heterogeneity, that is, the mediated moderation. For assessing mediated moderation, conventional methods typically require parametric models to define mediated moderation, which has limitations when parametric models may be misspecified and when causal interpretation is of interest. For causal interpretations about mediation, causal mediation analysis is increasingly popular but is underdeveloped for mediated moderation analysis. In this study, we extend the causal mediation literature, and we propose a novel method for mediated moderation analysis. Using the potential outcomes framework, we obtain two causal estimands that decompose the total moderation: (i) the mediated moderation attributable to a mediator and (ii) the remaining moderation unattributable to the mediator. We also develop a multiply robust estimation method for the mediated moderation analysis, which can incorporate machine learning methods in the inference of the causal estimands. We evaluate the proposed method through simulations. We illustrate the proposed mediated moderation analysis by assessing the mediation mechanism that underlies the gender difference in the effect of a preventive intervention on adolescent behavioral outcomes.
