Network Structural Equation Models for Causal Mediation and Spillover Effects

TL;DR

The robustness and practical utility of the methodology are demonstrated through simulation experiments and an analysis of the Twitch Gamers Network, underscoring its effectiveness in quantifying intricate network-mediated exposure effects.

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.

Figures (5)

• Figure 1: We consider a setup where $N=5$. Each node or DAG-clique consists of a triplet $(A,M,Y)$. The relationship between a DAG-clique $i$ and $j$, where $i\neq j$ and $i,j\in\mathcal{V}=\{1,2,3,4,5\}$ is characterized by the elements $E_{ij}$ of the adjacency matrix $E$ of network connectivity.
• Figure 2: Different mechanistic pathways arising from the exposures of unit 1, its first degree and second degree neighbors, to the outcome of unit 1, where units 2 and 4 are regarded as representatives of first and second degree neighbors of unit 1, respectively, according to the network topology given in Figure \ref{['fig:DAG1']}.
• Figure 3: Six DAGs represent the mediation and interference pathways for the corresponding six estimands, $\tau_1,\tau_2,\tau_3,\tau_4,\tau_5,\tau_6$, respectively with individual's self exposure ($A$), self mediator ($M$), self response ($Y$), neighborhood exposure ($\boldsymbol A_{\mathcal{N}^{\dagger}}$), neighbourhood mediator ($\boldsymbol M_{\mathcal{N}^{\dagger}}$). These DAGs do not contain the confounders for simplicity.
• Figure S1: Network Examples under the two simulation setups generated using sample size, $N=10$ for the purpose of illustration. The nodes are present on the circumference of the circle, where $i^{\text{th}}$ and $j^{\text{th}}$ nodes are connected if $E_{ij}=1$ and the self loops are omitted. For simulation setup 2, we used $p=0.4$ to generate the network under Erdos-Renyi Random Model.
• Figure S2: Mean Estimates of each of the six causal estimands along with 95% C.I applied to the Twitch Network Dataset. In this analysis we study the impact of mature content—both from individual users and the average within their network neighbors—on the views received by a user’s account mediated via the lifetimes of both the individual and neighbors' accounts.

Theorems & Definitions (19)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Theorem 1
• Corollary 1
• Corollary 2
• Theorem 2
• Theorem 3