Complementary strengths of the Neyman-Rubin and graphical causal frameworks

Abstract: This article contributes to the discussion on the relationship between the Neyman-Rubin and the graphical frameworks for causal inference. 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 application of the Neyman-Rubin approach is complicated, but the graphical approach is directly usable. 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.