Network Structural Equation Models for Causal Mediation and Spillover Effects

Ritoban Kundu; Peter X. K. Song

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arXiv · 2412.05397

Network Structural Equation Models for Causal Mediation and Spillover Effects

Ritoban Kundu·Peter X. K. Song

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Abstract

Social network interference induces complex dependencies where a unit's outcome is influenced not only by its own exposure and mediator but also by those of connected neighbors. In such settings, a significant challenge lies in distinguishing direct exposure effects from interference-driven spillover effects, and further separating these from indirect effects mediated by intermediate variables. To address this, we propose a theoretical framework utilizing structural graphical models. Central to our approach is the Random Effects Network Structural Equation Model (REN-SEM), which extends the exposure mapping paradigm to capture these multifaceted spillover and mediation mechanisms while accounting for latent dependencies within mediators and outcomes. We establish general identification conditions and derive decomposition formulas for six distinct mechanistic estimands. Furthermore, for the class of Linear REN-SEMs, we develop a maximum likelihood estimation framework and establish a rigorous asymptotic theory tailored to non-i.i.d. network data, proving the consistency of our estimators and the validity of the variance estimates. The robustness and practical utility of our methodology are demonstrated through simulation experiments and an analysis of the Twitch Gamers Network, underscoring its effectiveness in quantifying intricate network-mediated exposure effects.

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Ritoban Kundu, Peter X. K. Song. 2026-02-28. Network Structural Equation Models for Causal Mediation and Spillover Effects. https://arxiv.org/abs/2412.05397

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