Parametric and Non-Parametric Weighting Methods for Mediation Analysis: An Application to the National Evaluation of Welfare-to-Work Strategies

This study analyzes the impact of a welfare-to-work program on maternal depression mediated by employment experience in the context of a randomized experiment. We develop parametric and non-parametric weighting procedures as alternative strategies for removing selection bias in estimating the controlled direct effect of the policy and that of the mediator. Through ratio-of-mediator-probability weighting, we further decompose the total effect into a natural direct effect and a natural indirect effect. Simulation results suggest that the parametric and non-parametric weighting methods both have satisfactory performance when the propensity score models are correctly specified. The weighting results replicate those from path analysis and the Instrumental Variable method when the assumption of no treatment-by-mediator interaction and the exclusion restriction hold. The weighting methods show great advantages when these assumptions do not hold. Additionally, the weighting approach is exempted from assuming the distribution of the outcome, the distribution of the mediator, and the functional form of the outcome model. Hence it provides a viable alternative to the model-based approaches.