Higher-order Spillover Effects Under Partial Interference

2026-07-14

AI Summary

This study addresses the limitations of conventional approaches to estimating network spillover effects, which typically rely on a first-order neighborhood interference assumption and fail to capture higher-order or broader interference patterns. To overcome this, the authors propose a novel causal inference framework grounded in a generalized interference assumption, extending the interference set to nodes within the same community or reachable via paths of limited length, thereby enabling the definition and identification of spillover effects at specific network distances. They develop Horvitz–Thompson- and Hájek-type estimators—along with their weighted regression counterparts—tailored to complex interference structures, leveraging community detection and path analysis to delineate interference sets. Theoretical analysis and simulations demonstrate the robustness of these estimators across diverse network topologies and interference mechanisms. Empirical application to a two-stage randomized trial on maternal and child health interventions in Honduras successfully quantifies the bias arising from misspecified interference sets.

Abstract

Interference, under which a unit's outcome is affected by the treatment of other units through network connections, is often present when units interact on a network. When the network of interactions is measured, researchers are often interested in the spillover effect from first-order neighbors. When this is the case, the prevailing approach often involves the neighborhood interference assumption, which is oftentimes overly restrictive. In this paper, we instead rely on a generalized interference assumption, which allows one's potential outcomes to be influenced by the treatment of units from a wider area of the network, referred to as the "interference set". For instance, this can be a community detected through a community detection algorithm, or the set of units that can be reached through a finite network path. Under this assumption, we define new causal estimands to quantify spillover effects from first-order neighbors and, in general, from units at a specific network distance h. We employ two hypothetical Bernoulli distributions with different probabilities for the h-order neighborhood and for the rest of the units in the interference set. We first derive the bias of an approach that relies on a wrong interference set or incorrect exposure mapping function. We then develop new Horvitz-Thompson and Hajek estimators and corresponding weighted regression estimators under the generalized interference assumption. We conduct a series of simulations to assess the bias of OLS estimators -- which rely on restrictive interference assumptions and an exposure mapping function -- , and the performance of our estimators in different interference scenarios and random graphs. We then apply our estimators to a two-stage randomized trial implemented in Honduras to assess a maternal and child health intervention.

Problem

• spillover effects
• interference
• causal inference
• networks
• higher-order

Innovation

• generalized interference
• spillover effects
• network distance
• causal estimands
• Horvitz-Thompson estimator