Statistical Tests for Contagion in Observational Social Network Studies

Current tests for contagion in social network studies are vulnerable to the confounding effects of latent homophily (i.e., ties form preferentially between individuals with similar hidden traits). We demonstrate a general method to lower bound the strength of causal effects in observational social network studies, even in the presence of arbitrary, unobserved individual traits. Our tests require no parametric assumptions and each test is associated with an algebraic proof. We demonstrate the effectiveness of our approach by correctly deducing the causal effects for examples 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 contagion in observational social network studies (see, e.g., this recent review [2]). The most general result from the causal modeling perspective shows that latent homophily acts as a confounder for contagion so that uniquely pinpointing the strength of contagion is impossible 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 intervention is often impractical or even unethical. MeaAppearing in Proceedings of the 16 International Conference on Artificial Intelligence and Statistics (AISTATS) 2013, Scottsdale, AZ, USA. Volume 31 of JMLR: W&CP 31. Copyright 2013 by the authors. suring all the human traits that affect link formation and observed actions is unrealistic. A method to measure the strength of causal effects without recourse to these alternatives is of central importance for studying social networks. Our method produces a sequence of bounds on the strength of contagion which converge in some limit to the best possible bounds. In this sense, our method is the best solution to the problem of measuring the strength of contagion that does not involve invoking additional (parametric) assumptions.