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How many people do you know in prison?: using overdispersion in count data to estimate social structure in networks Zheng, Tian Salganik, Matt Gelman, Andrew Uploaded 10-12-2005 Keywords negative binomial distribution overdispersion sampling social networks social structure Abstract Networks--sets of objects connected by relationships--are important in a number of fields. The study of networks has long been central to sociology, where researchers have attempted to understand the causes and consequences of the structure of relationships in large groups of people. Using insight from previous network research, Killworth et al. (1998a,b) and McCarty et al. (2001) developed and evaluated a method for estimating the sizes of hard-to-count populations using network data collected from a simple random sample of Americans. In this paper we show how, using a multilevel overdispersed Poisson regression model, these data can also be used to estimate aspects of social structure in the population. Our work goes beyond most previous research on networks by using variation, as well as average responses, as a source of information. We apply our method to the McCarty et al. data and find that Americans vary greatly in their number of acquaintances. Further, Americans show great variation in propensity to form ties to people in some groups (e.g., males in prison, the homeless, and American Indians), but little variation for other groups (e.g., twins, people named Michael or Nicole). We also explore other features of these data and consider ways in which survey data can be used to estimate network structure.

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The “Unfriending” Problem: The Consequences of Homophily in Friendship Retention for Causal Estimates of Social Influence Noel, Hans Nyhan, Brendan Uploaded 07-08-2010 Keywords peer effects social networks monte carlo homophily contagion simulation Abstract Christakis, Fowler, and their colleagues have recently published numerous articles estimating “contagion” effects in social networks. In response to concerns that their results are driven by homophily, Christakis and Fowler describe Monte Carlo results showing no evidence of homophily-induced bias in their statistical model’s estimates of peer effects. However, their simulations do not address the role of homophily in friendship retention, which may cause significant problems in longitudinal social network data. We investigate the effects of this mechanism using Monte Carlo simulations and demonstrate that homophily in friendship retention induces significant upward bias and decreased coverage levels in the Christakis and Fowler model if there is non-negligible attrition over time.