TY - JOUR
T1 - How many people do you know in prison?
T2 - Using overdispersion in count data to estimate social structure in networks
AU - Zheng, Tian
AU - Salganik, Matthew J.
AU - Gelman, Andrew
N1 - Funding Information:
Tian Zheng is Assistant Professor, Department of Statistics (E-mail: [email protected]), Andrew Gelman is Professor, Department of Statistics and Department of Political Science (E-mail: [email protected]. edu), and Matthew J. Salganik is a Doctoral Student, Department of Sociology and Institute for Social and Economic Research and Policy (E-mail: [email protected]), Columbia University, New York, NY 10027. The authors thank Peter Killworth and Chris McCarty for the survey data on which this study was based, and Francis Tuerlinckx, Tom Snijders, Peter Bearman, Michael Sobel, Tom DiPrete, and Erik Volz for helpful discussions. They also thank three anonymous reviewers for their constructive suggestions. This research was supported by the National Science Foundation, a Fulbright Fellowship, and the Netherland–America Foundation. The material presented in this article is partly based on work supported under a National Science Foundation Graduate Research Fellowship.
PY - 2006/6
Y1 - 2006/6
N2 - 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. and McCarty et al. have 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 article we show how, using a multilevel overdispersed Poisson regression model, these data also can 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 data of McCarty et al. 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.
AB - 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. and McCarty et al. have 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 article we show how, using a multilevel overdispersed Poisson regression model, these data also can 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 data of McCarty et al. 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.
KW - Negative binomial distribution
KW - Overdispersion
KW - Sampling
KW - Social networks
KW - Social structure
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U2 - 10.1198/016214505000001168
DO - 10.1198/016214505000001168
M3 - Article
AN - SCOPUS:33745638530
SN - 0162-1459
VL - 101
SP - 409
EP - 423
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 474
ER -