Comments: Improving Weighting Methods for Causal Mediation Analysis

I begin this discussion by thanking Larry Hedges, the editor of the journal, for giving me an opportunity to provide a commentary on this stimulating article. I also would like to congratulate the authors of the article for their insightful discussion on causal mediation analysis, which is one of the most important and challenging methodological problems we face in the literature of causal inference. I particularly admire the authors’ efforts to clearly explain complex statistical concepts in the context of their specific application. I have no doubt that applied education researchers who read this article will gain a better understanding of important methodological issues regarding causal mediation analysis. Although there are many positive things to be said about the authors’ proposed methodology, in this commentary I discuss one potential way to further improve it. In particular, the authors argue that the proposed ratio-of-mediator-probability weighted (RMPW) estimation methodology is attractive because unlike some of the existing methods it “does not involve explicit modeling of the mediator-outcome relationship” (p. 273). Although this is clearly an advantage, the RMPW estimation methodology still requires researchers to correctly model the mediator given the treatment and pretreatment confounders. This is often a challenging task because there may exist a large number of pretreatment confounders. Because nonparametric modeling in a high-dimensional covariate space is difficult, these confounders often must be adjusted through a parametric model. A similar problem applies to propensity score methods. For example, Kang and Schafer (2007) showed that slight misspecification of propensity score model can yield a large bias in the estimation of treatment effects. They found that the magnitude of such bias can be quite substantial for propensity score weighting methods when the severe selection bias leads to small weights. Imai King and Stuart (2008) called this problem “propensity score tautology”—propensity score methods allow researchers to avoid the modeling of the outcome-treatment relationship only when they can correctly model the treatment-covariate relationship. The proposed RMPW estimation methodology resembles propensity score weighting methods in that researchers must confront the equally difficult task of correctly modeling the conditional distribution of mediator given the treatment and pretreatment confounders. To address this issue, Imai and Ratkovic (2012) proposed the covariate balancing propensity score (CBPS) estimation as the robust parametric estimation strategy for the propensity score. The idea is to exploit the dual characteristics of the propensity score as the conditional probability of treatment assignment and a balancing score: If the propensity score is correctly estimated, it should predict the treatment assignment Z and balance the covariate distribution between the treatment and control groups (once the covariates X