Statistical Tests for Contagion in Observational Social Network Studies

Current tests for contagion in social network studies are vulnerable to the confounding ef-fects of latent homophily (i.e., ties form pref-erentially between individuals with similar hidden traits). We demonstrate a general method to lower bound the strength of causal effects in observational social network stud-ies, even in the presence of arbitrary, unob-served individual traits. Our tests require no parametric assumptions and each test is as-sociated with an algebraic proof. We demon-strate the effectiveness of our approach by correctly deducing the causal effects for ex-amples previously shown to expose defects in existing methodology. Finally, we discuss preliminary results on data taken from the Framingham Heart Study. Christakis and Fowler’s paper suggesting that obesity may spread along social ties [3] has sparked years of discussion about what constitutes evidence of conta-gion in observational social network studies (see, e.g., this recent review [2]). The most general result from the causal modeling perspective shows that latent ho-mophily acts as a confounder for contagion so that uniquely pinpointing the strength of contagion is im-possible without additional assumptions [14]. In other words, contagion is non-parametrically unidentifiable. However, if the true goal is to test for the presence of contagion, a lower bound on the strength of contagion is all that is necessary. We present a general method to obtain such bounds in this paper. Identifying causal effects in social networks through in-tervention is often impractical or even unethical. Mea