A Regression-with-Residuals Method for Estimating Controlled Direct Effects

Political scientists are increasingly interested in causal mediation, and to this end, recent studies focus on estimating a quantity called the controlled direct effect (CDE). The CDE measures the strength of the causal relationship between a treatment and outcome when a mediator is fixed at a given value. To estimate the CDE, Joffe and Greene (2009) and Vansteelandt (2009) developed the method of sequential g-estimation, which was introduced to political science by Acharya, Blackwell, and Sen (2016). In this letter, we propose an alternative method called “regression-with-residuals” (RWR) for estimating the CDE. In special cases, we show that these two methods are algebraically equivalent. Yet, unlike sequential g-estimation, RWR can easily accommodate several types of effect moderation, including cases in which the effect of the mediator on the outcome is moderated by a posttreatment confounder. Although common in the social sciences, this type of effect moderation is typically assumed away in applications of sequential g-estimation, which may lead to bias if effect moderation is in fact present. We illustrate RWR by estimating the CDE of negative media framing on public support for immigration, controlling for respondent anxiety.