Partial identification of principal causal effects under violations of principal ignorability

2024-12-09

AI Summary

This paper addresses partial identification of principal causal effects when the Principal Stratification Ignorability (PSI) assumption fails. To overcome the limitation of existing joint modeling approaches—which yield only partial identification even under known joint stratum distributions and correctly specified outcome models—we propose novel identification conditions strictly weaker than PSI, establishing for the first time a theoretical linkage between the identifiability of association parameters and the degree of PSI violation. Methodologically, we unify parametric, semiparametric, and nonparametric Bayesian modeling within the principal stratification framework, enabling more flexible model specifications. Our main contributions are threefold: (1) a rigorous proof that principal causal effects are always partially identifiable under arbitrary PSI violations; (2) derivation of tighter partial identification intervals compared to conventional methods; and (3) demonstration that association parameters are identifiable only under stringent functional-form restrictions, thereby revealing their intrinsic nonidentifiability.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Security and Privacy: Large-scale security measurements

Abstract

Principal stratification is a general framework for studying causal mechanisms involving post-treatment variables. When estimating principal causal effects, the principal ignorability assumption is commonly invoked, which we study in detail in this manuscript. Our first key contribution is studying a commonly used strategy of using parametric models to jointly model the outcome and principal strata without requiring the principal ignorability assumption. We show that even if the joint distribution of principal strata is known, this strategy necessarily leads to only partial identification of causal effects, even under very simple and correctly specified outcome models. While principal ignorability can lead to point identification in this setting, we discuss alternative, weaker assumptions and show how they lead to more informative partial identification regions. An additional contribution is that we provide theoretical support to strategies used in the literature for identifying association parameters that govern the joint distribution of principal strata. We prove that this is possible, but only if the principal ignorability assumption is violated. Additionally, due to partial identifiability of causal effects even when these association parameters are known, we show that these association parameters are only identifiable under strong parametric constraints. Lastly, we extend these results to more flexible semiparametric and nonparametric Bayesian models.

Problem

• Estimating principal causal effects without principal ignorability assumption
• Exploring partial identification under weaker alternative assumptions
• Identifying association parameters under violated principal ignorability

Innovation

• Parametric models for outcome and principal strata
• Partial identification without principal ignorability
• Semiparametric and nonparametric Bayesian extensions