Complementary Strengths of the Neyman–Rubin and Graphical Causal Frameworks

We present specific examples of data-generating mechanisms—such as those involving undirected or deterministic relationships and cycles—where analyses using a directed acyclic graph are challenging, but where the tools from the Neyman–Rubin causal framework are readily applicable.

We also provide examples of data-generating mechanisms with M-bias, trapdoor variables, and complex front-door structures, where the covariate adjustment in the Neyman–Rubin approach provides biased estimators of causal effects, but the graphical approach helps analysts identify valid strategies for unbiased estimation. The examples offer insights into commonly used causal inference frameworks and aim to improve comprehension of the languages for causal reasoning among a broad audience.</p>