Possibilistic Instrumental Variable Regression

2025-11-19

AI Summary

In practice, instrumental variable (IV) exogeneity is often unverifiable due to unobserved confounding, and researchers frequently face settings with only a single, potentially invalid IV. Method: This paper proposes a possibility-theoretic IV regression framework that relaxes the strict exogeneity assumption by modeling potential violations as possibility distributions—enabling posterior inference on the treatment effect and systematic sensitivity analysis even with one possibly invalid IV. Contribution/Results: Unlike conventional Bayesian or robust IV approaches, our framework provides a principled, non-probabilistic foundation for causal inference under weak or suspect instruments. Simulation studies and empirical applications demonstrate its high robustness and inferential richness under multiple challenges—including IV invalidity, weak instrument strength, and strong unmeasured confounding—thereby substantially broadening the applicability boundary of IV-based causal inference.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the exogeneity assumption. Our method can provide informative results even when only a single, potentially invalid, instrument is available, offering a natural and principled framework for sensitivity analysis. Simulation experiments and a real-data application indicate strong performance of the proposed approach.

Problem

• Addresses causal inference with unobserved confounding variables
• Proposes possibilistic method for invalid instrumental variables
• Enables sensitivity analysis with single potentially invalid instrument

Innovation

• Uses possibility theory for posterior inference
• Analyzes treatment effects with potential exogeneity violations
• Works with single potentially invalid instruments