Complete Graphical Characterization and Construction of Adjustment Sets in Markov Equivalence Classes of Ancestral Graphs

TL;DR

This paper introduces a unified graphical criterion for covariate adjustment across multiple causal graph classes, providing explicit sets, efficient algorithms, and theoretical proofs to enhance causal inference methods.

Contribution

It presents a complete and sound graphical criterion for adjustment in various causal graph classes, along with algorithms and proofs, unifying and extending existing adjustment methods.

Findings

Unified adjustment criterion for DAGs, MAGs, CPDAGs, and PAGs

Efficient algorithms for constructing adjustment sets

Implementation in R package dagitty

Abstract

We present a graphical criterion for covariate adjustment that is sound and complete for four different classes of causal graphical models: directed acyclic graphs (DAGs), maximum ancestral graphs (MAGs), completed partially directed acyclic graphs (CPDAGs), and partial ancestral graphs (PAGs). Our criterion unifies covariate adjustment for a large set of graph classes. Moreover, we define an explicit set that satisfies our criterion, if there is any set that satisfies our criterion. We also give efficient algorithms for constructing all sets that fulfill our criterion, implemented in the R package dagitty. Finally, we discuss the relationship between our criterion and other criteria for adjustment, and we provide new soundness and completeness proofs for the adjustment criterion for DAGs.