Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractions
It addresses foundational issues in causal inference for researchers, but is incremental as it builds on prior logical work to reconcile existing frameworks.
This paper clarifies the relationship between the Rubin causal model (RCM) and structural causal model (SCM) frameworks for causal inference, showing that every RCM can be represented as an abstraction of some SCM and highlighting mutual applications between the frameworks.
The aim of this paper is to make clear and precise the relationship between the Rubin causal model (RCM) and structural causal model (SCM) frameworks for causal inference. Adopting a neutral logical perspective, and drawing on previous work, we show what is required for an RCM to be representable by an SCM. A key result then shows that every RCM -- including those that violate algebraic principles implied by the SCM framework -- emerges as an abstraction of some representable RCM. Finally, we illustrate the power of this conciliatory perspective by pinpointing an important role for SCM principles in classic applications of RCMs; conversely, we offer a characterization of the algebraic constraints implied by a graph, helping to substantiate further comparisons between the two frameworks.