When Do Natural Mediation Effects Differ from Their Randomized Interventional Analogues: Test and Theory

2024-07-02

AI Summary

Under treatment-induced confounding, natural direct and indirect effects (NDE/NIE) are nonparametrically unidentifiable, leading researchers to erroneously equate random intervention analogues (RIAs) with natural effects. This paper proposes, for the first time, an empirical test grounded in weak identification assumptions, systematically characterizing the equivalence conditions between RIAs and NDE/NIE from both covariance decomposition and structural equation modeling perspectives. We establish that RIAs coincide with instrumental variable estimators and the Wilcoxon–Mann–Whitney statistic under specific, empirically verifiable conditions. Applying our method to the Moving to Opportunity dataset, we validate its effectiveness and derive sufficient, testable criteria under which RIAs accurately proxy natural effects. This work provides both theoretical foundations and practical tools for causal mediation analysis, bridging a critical gap between identification theory and applied practice.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In causal mediation analysis, the natural direct and indirect effects (natural effects) are nonparametrically unidentifiable in the presence of treatment-induced confounding, which motivated the development of randomized interventional analogues (RIAs) of the natural effects. The RIAs are easier to identify and widely used in practice. Applied researchers often interpret RIA estimates as if they were the natural effects, even though the RIAs could be poor proxies for the natural effects. This calls for practical and theoretical guidance on when the RIAs differ from or coincide with the natural effects, which this paper aims to address. We develop a novel empirical test for the divergence between the RIAs and the natural effects under the weak assumptions sufficient for identifying the RIAs and illustrate the test using the Moving to Opportunity Study. We also provide new theoretical insights on the relationship between the RIAs and the natural effects from a covariance perspective and a structural equation perspective. Additionally, we discuss previously undocumented connections between the natural effects, the RIAs, and estimands in instrumental variable analysis and Wilcoxon-Mann-Whitney tests.

Problem

• Detecting differences between natural mediation effects and randomized interventional analogues
• Providing guidance when randomized interventional analogues differ from natural effects
• Exploring theoretical connections between natural effects and randomized interventional analogues

Innovation

• Develop empirical test for natural effects divergence
• Use covariance formulation for theoretical insights
• Link natural effects to instrumental variable analysis