🔍 What This Paper Proposes
Political scientists increasingly focus on causal mediation and, in particular, the controlled direct effect (CDE) — the causal effect of a treatment on an outcome when a mediator is fixed at a specific value. This paper introduces an alternative estimation approach called regression-with-residuals (RWR) for estimating the CDE.
🔬 How the new method fits with existing tools
- Sequential g-estimation was developed for this task by Joffe and Greene (2009) and Vansteelandt (2009) and was introduced to political science audiences by Acharya, Blackwell, and Sen (2016).
- In special cases, RWR is algebraically equivalent to sequential g-estimation, showing that RWR nests familiar solutions under certain assumptions.
📌 What RWR does differently
- RWR easily accommodates several types of effect moderation, including situations where the mediator's effect on the outcome is moderated by a posttreatment confounder.
- Such moderation is common in the social sciences but is typically assumed away in applications of sequential g-estimation; ignoring it can produce biased CDE estimates.
📊 Evidence and illustration
- Mathematical comparisons demonstrate algebraic equivalence between RWR and sequential g-estimation in special cases.
- Analytical arguments show RWR’s flexibility for modeling effect moderation that sequential g-estimation usually cannot handle without additional assumptions.
- An applied example estimates the CDE of negative media framing on public support for immigration while controlling for respondent anxiety to illustrate RWR in practice.
🔑 Why it matters
- Accurate CDE estimation matters for causal claims about policy and communication effects. RWR offers a practical, accessible alternative that preserves correct inference when effect moderation by posttreatment confounders is present.
