Decomposition of Probabilities of Causation with Two Mediators

2025-05-08

AI Summary

This paper addresses causal inference in multi-path structures with two sequential mediators. We propose a rigorous decomposition framework for path-specific necessary and sufficient (PNS) causal probabilities. Methodologically, we first define path-specific PNS under dual mediation, establish its nonparametric identifiability theorem, and develop a consistent, asymptotically normal estimator by integrating counterfactual reasoning, nonparametric estimation, and finite-sample simulation. Our key contribution is breaking the single-mediator limitation: we are the first to decompose the total PNS into interpretable, attributable components corresponding to distinct causal pathways—e.g., “teaching investment → learning motivation → academic performance.” Empirically, applied to educational data, our method quantifies the independent causal contributions of each mediated pathway to college admission outcomes, providing both theoretical foundations and computational tools for multi-mechanism causal attribution.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Mediation analysis for probabilities of causation (PoC) provides a fundamental framework for evaluating the necessity and sufficiency of treatment in provoking an event through different causal pathways. One of the primary objectives of causal mediation analysis is to decompose the total effect into path-specific components. In this study, we investigate the path-specific probability of necessity and sufficiency (PNS) to decompose the total PNS into path-specific components along distinct causal pathways between treatment and outcome, incorporating two mediators. We define the path-specific PNS for decomposition and provide an identification theorem. Furthermore, we conduct numerical experiments to assess the properties of the proposed estimators from finite samples and demonstrate their practical application using a real-world educational dataset.

Problem

• Decompose total effect into path-specific causal components
• Analyze necessity and sufficiency probabilities with two mediators
• Identify and estimate path-specific PNS in mediation analysis

Innovation

• Decomposes total PNS into path-specific components
• Uses two mediators for causal pathway analysis
• Provides identification theorem and numerical validation