Causal Inference for Network Autoregression Model: A Targeted Minimum Loss Estimation Approach

TL;DR

This paper develops a novel targeted minimum loss estimation (TMLE) method for estimating the average treatment effect in network settings with interference, accounting for complex dependence structures and providing theoretical and empirical validation.

Contribution

It introduces a TMLE approach tailored for network autoregressive models with infinite interference, including new limit theory and variance estimation guarantees.

Findings

Achieves smaller asymptotic variance than existing methods under certain conditions.

Develops a new limit theory for complex network-dependent asymptotics.

Demonstrates advantages through numerical studies and real data analysis.

Abstract

We study estimation of the average treatment effect (ATE) from a single network in observational settings with interference. The weak cross-unit dependence is modeled via an endogenous peer-effect (network autoregressive) term that induces distance-decaying network dependence, relaxing the common finite-order interference to infinite interference. We propose a targeted minimum loss estimation (TMLE) procedure that removes plug-in bias from an initial estimator. The targeting step yields an adjustment direction that incorporates the network autoregressive structure and assigns heterogeneous, network-dependent weights to units. We find that the asymptotic leading term related to the covariates $\mathbf{X}_i$ can be formulated into a $V$-statistic whose order diverges with the network degrees. A novel limit theory is developed to establish the asymptotic normality under such complex network dependent scenarios. We show that our method can achieve smaller asymptotic variance than existing methods when $\mathbf{X}_i$ is i.i.d. generated and estimated with empirical distribution, and provide theoretical guarantees for estimating the variance. Extensive numerical studies and a live-streaming data analysis are presented to illustrate the advantages of the proposed method.