A Sensitivity Framework for Identifying Contagion under Latent Homophily for Fixed-in-Time Network Analyses, with an Application to U.S. House Congressional Voting

Abstract: Whether connected units are similar because influence spreads across ties or because similar units form ties, is a long-standing problem. Contagion or influence is generically unidentified from observational network data. We consider the minimal and common setting of a single network, fixed over time, with two waves of a binary nodal outcome. Rather than positing a parametric model for network formation, we reframe identification of contagion as a selection-bias problem and develop a sensitivity framework. We define a controlled direct effect (CDE) holding a tie present while intervening on an alter's outcome. We show that the gap between the CDE and the observed connected-dyad risk ratio is governed by how strongly a latent homophily variable shifts the composition of connected dyads. Inspired by Smith-style selection-bias sensitivity analysis and the risk-ratio bounding function of Ding and VanderWeele we develop interpretable nonparametric bounds. This translates the question "is there contagion?" into the question "how strong would latent homophily have to be to explain away the observed contagion?" A simulation study characterizes the bounds' error control and power. We apply the framework to the 2008 U.S. House votes on the Troubled Asset Relief Program, identifying under which assumptions contagion is plausible.