The "Unfriending" Problem: The Consequences of Homophily in Friendship Retention for Causal Estimates of Social Influence

Abstract: An increasing number of scholars are using longitudinal social network data to try to obtain estimates of peer or social influence effects. These data may provide additional statistical leverage, but they can introduce new inferential problems. In particular, while the confounding effects of homophily in friendship formation are widely appreciated, homophily in friendship retention may also confound causal estimates of social influence in longitudinal network data. We provide evidence for this claim in a Monte Carlo analysis of the statistical model used by Christakis, Fowler, and their colleagues in numerous articles estimating "contagion" effects in social networks. Our results indicate that homophily in friendship retention induces significant upward bias and decreased coverage levels in the Christakis and Fowler model if there is non-negligible friendship attrition over time.