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

Statistics > Applications [Submitted on 16 Jun 2026] Title:A Sensitivity Framework for Identifying Contagion under Latent Homophily for Fixed-in-Time Network Analyses, with an Application to U.S. House Congressional Voting View PDF HTML (experimental)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. Current browse context: stat.AP References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.