My apologies to Andrew's co-authors:  The correct citation is the
following.
-KJ

title:         How many people do you know in prison?: using overdispersion in count data to estimate social structure in networks
authors:       tian zheng, matt salganik, Andrew Gelman
entrydate:     2005-10-12 17:22:23
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.

http://polmeth.wustl.edu/retrieve.php?id=564

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