Spillover Effects in the Presence of Unobserved Networks

Abstract

When experimental subjects can interact with each other, the outcome of one individual may be affected by the treatment status of others. In many social science experiments, such spillover effects may occur through multiple networks, for example, through both online and offline face-to-face networks in a Twitter experiment. Thus, to understand how people use different networks, it is essential to estimate the spillover effect in each specific network separately. However, the unbiased estimation of these network-specific spillover effects requires an often-violated assumption that researchers observe all relevant networks. We show that, unlike conventional omitted variable bias, bias due to unobserved networks remains even when treatment assignment is randomized and when unobserved networks and a network of interest are independently generated. We then develop parametric and nonparametric sensitivity analysis methods, with which researchers can assess the potential influence of unobserved networks on causal findings. We illustrate the proposed methods with a simulation study based on a real-world Twitter network and an empirical application based on a network field experiment in China.

Methods for Assessing Spillover in Network-Based Studies of HIV/AIDS Prevention among People Who Use Drugs

“…In addition, if the spillover set actually included two-degree neighbors or other sets of individuals in the network, the nearest-neighbor interference assumption would not be valid. We recommend extensions to the methods that consider alternative definitions of the spillover set in the network and assess the extent to which results change under alternative assumptions on the spillover sets [ 92 , 93 ]. When information on the true social relationships is only available for a subset of the sample, validation study/main study bias correction methods could be used to correct for the bias resulting from the definition of spillover sets based on the available information on randomization clusters or geographical distances.…”

“…In this randomized design, one approach to estimate spillover effects is a Horvitz–Thompson type estimator with unequal probability sampling with inverse probability weighted (IPW) estimators, and conservative variance estimators have been proposed [ 64 ]. Although randomization provides protection against confounding, randomized designs can be vulnerable to other issues, including generalizability [ 91 ], measurement error of spillover sets [ 92 , 93 ], non-compliance [ 84 ], and selection bias due to differential loss to follow-up [ 94 , 95 ], that warrant further consideration when evaluating spillover (see Section 3.5.2 ).…”

Recent Developments in Causal Inference and Machine Learning

“…In such settings, one unit’s potential outcome is a function of not only its treatment status but also the treatment status of other related units ( Aronow & Samii 2017 , Athey et al 2018a , Tchetgen Tchetgen & VanderWeele 2012 , VanderWeele 2015 ). Such interferences, or interactions, are prevalent in social settings ( An 2018 , An & VanderWeele 2022 , Egami 2021 ). For example, encouraging an individual to vote through some intervention can increase the turnout for household members ( Imai & Jiang 2020 ).…”

Estimating Dynamic Spillover Effects along Multiple Networks in a Linear Panel Model

“…The perspective of spillover effects realizing along multiple networks has received attention in the literature. Egami (2021) developed methods of sensitivity analysis when there are unobserved networks that capture part of the spillover effects. Drukker, Egger, and Prucha (2022) proposed asymptotic analysis of estimation and inference procedures in a linear spatial model, which accommodates multiple networks.…”