Working Paper 2018-01

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

Xiang Zhou, Harvard University

Geoffrey T. Wodtke, University of Toronto

UT Sociology Working Paper No. 2018-01

March 2018

Keywords: Regression Analysis; Methods

Full Article


In a recent contribution, Acharya, Blackwell and Sen (2016) described the method of sequential g-estimation for estimating the controlled direct effect (CDE). We propose an alternative method, which we call ”regression-with-residuals” (RWR), for estimating the CDE. Compared with sequential g-estimation, the RWR method is easier to understand and to implement. Moreimportant, unlike sequential g-estimation, it can easily accommodate several different types of effect moderation, including cases in which the effect of the mediator on the outcome is moderated by a post-treatment, or intermediate, 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 reanalyzing the effect of plough use on female political participation while allowing the effect of log GDP per capita (the mediator) to vary across levels of several intermediate confounders.