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

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.

💡 Research Summary

The paper investigates a subtle source of bias that can arise when researchers use longitudinal social‑network data to estimate peer influence. Christakis and Fowler (CF) have popularized a generalized estimating‑equation (GEE) approach that controls for the baseline similarity of ego and alter (the “homophily” in tie formation) and then interprets the coefficient on the alter’s later outcome as a causal contagion effect. The authors of the present study argue that this strategy overlooks homophily in friendship retention – the tendency for similar individuals to stay friends while dissimilar ones are more likely to “unfriend.” Because most longitudinal network panels exhibit non‑trivial attrition, the process of unfriending can be systematically related to changes in the trait of interest, creating a spurious correlation between ego’s outcome at the second wave and alter’s outcome at the same wave that is not captured by the lagged covariates.

To assess the magnitude of this problem, the authors replicate the Monte‑Carlo simulation framework used by CF, but they deliberately set the true peer‑effect parameter to zero. They generate a population of 1,000 actors with a normally distributed trait, construct dyadic ties with a probability that increases with similarity, and then impose a second‑wave attrition rule in which dyads with larger trait differences are more likely to dissolve. The simulation therefore embeds homophily in both tie formation and tie dissolution while keeping the underlying social influence absent.

The results show that when friendship attrition is present, the CF estimator produces a positive bias in the estimated peer‑effect coefficient that grows with the strength of homophily in retention. Moreover, the nominal 95 % confidence intervals cover the true zero value far less often than they should, indicating severe under‑coverage. In other words, researchers applying the CF model to data with realistic levels of unfriending are likely to conclude that a contagion effect exists even when none does.

The paper concludes that the “unfriending” problem constitutes a serious threat to causal inference in observational network studies. It recommends two broad remedies: (1) explicitly model the friendship‑retention process, for example by incorporating a selection equation for tie survival or by using methods that jointly estimate formation, dissolution, and influence; and (2) collect detailed information on tie status at each wave so that non‑random attrition can be accounted for in the analysis. The authors also caution that many of the high‑profile findings on obesity, smoking, happiness, and other outcomes reported by CF and others may be at least partly driven by this overlooked source of bias.

Overall, the study highlights that homophily is not confined to the moment of tie creation; it persists in the maintenance of relationships and can masquerade as peer influence when longitudinal data are analyzed with models that ignore it.