Causal moderated mediation analysis: Methods and software.

Research questions regarding how, for whom, and where a treatment achieves its effect on an outcome have become increasingly valued in substantive research. Such questions can be answered by causal moderated mediation analysis, which assesses the heterogeneity of the mediation mechanism underlying the treatment effect across individual and contextual characteristics. Various moderated mediation analysis methods have been developed under the traditional path analysis/structural equation modeling framework. One challenge is that the definitions of moderated mediation effects depend on statistical models of the mediator and the outcome, and no solutions have been provided when either the mediator or the outcome is binary, or when the mediator or outcome model is nonlinear. In addition, it remains unclear to empirical researchers how to make causal arguments of moderated mediation effects due to a lack of clarifications of the underlying assumptions and methods for assessing the sensitivity to violations of the assumptions. This article overcomes the limitations by developing general definition, identification, estimation, and sensitivity analysis for causal moderated mediation effects under the potential outcomes framework. We also developed a user-friendly R package moderate.mediation ( https://cran.r-project.org/web/packages/moderate.mediation/index.html ) that allows applied researchers to easily implement the proposed methods and visualize the initial analysis results and sensitivity analysis results. We illustrated the application of the proposed methods and the package implementation with a re-analysis of the National Evaluation of Welfare-to-Work Strategies (NEWWS) Riverside data.