Signed directed acyclic graphs for causal inference.

Area of Science:

• Causal inference
• Graph theory
• Statistical modeling

Background:

• Causal directed acyclic graphs (DAGs) are foundational for causal inference.
• Reasoning about causality often requires understanding the direction and magnitude of effects.
• Existing methods may face challenges with intermediate variables or missing data.

Purpose of the Study:

• To introduce formal rules for signed edges in causal DAGs.
• To demonstrate the utility of these rules in causal reasoning.
• To extend causal inference capabilities in the presence of intermediate variables and missing data.

Main Methods:

• Introduction of formal rules for signed edges in causal DAGs.
• Definition of monotonic effect and weak monotonic effect.
• Development of results relating monotonic effects and signed edges to causal effect signs and covariance signs.

Main Results:

• Formal rules for signed edges in causal DAGs are established.
• Relationships between monotonic effects, signed edges, and the sign of causal effects with intermediate variables are derived.
• Rules connecting monotonic effects and covariance signs are developed.
• The framework allows causal effect conclusions with missing confounding data under certain assumptions.

Conclusions:

• Signed edges provide a formal mechanism for causal reasoning within DAGs.
• The developed rules enhance the ability to infer causal effects, particularly with complex structures.
• The approach offers a robust method for causal inference even when faced with data limitations.