Ruling out latent homophily in social networks

Despite recent high profile studies identifying counter-intuitive behaviors (e.g. obesity [3]) as being socially contagious, Shalizi and Thomas [12] have demonstrated that homophily on latent attributes is indistinguishable from influence. For sociologists to unequivocally identify influence effects in networks they must rule out the possibility of latent homophily as an explanation. This requires either undertaking the Sisyphean task of measuring every hidden attribute that might influence the formation of links in social networks or, our goal, determine the conditions for distinguishing influence from homophily even in the presence of unobserved attributes. Our test is inspired by the Bell inequalities: a simple inequality involving observed probability distributions which is obeyed by classical physics, but violated by quantum physics. We show any model producing correlations between actors through static latent homophily alone will obey certain constraints, and we develop and test a technique to detect violation of these constraints.