Statistical Modeling of Social Networks: Practical Advances and Results

Steven M. Goodreau, University of Washington
Martina Morris, University of Washington
Mark S. Handcock, University of Washington

Network modeling is becoming an increasingly important area of research in the social sciences with demographic applications in the population impacts of HIV/AIDS, contraceptive adoption, and chain migration. Statistical modeling of network data has been a challenge, due to sampling and dependence issues. This paper presents some recent advances in statistical network analysis, based on exponential random graph models. The models allow researchers to parameterize structural features of networks, such as degree distributions, assortative mixing, and network configurations like cycles and paths. These features have important practical implications for network sampling, and the methods represent a fundamental advance in network analysis. The methods are demonstrated with a comparative analysis of the friendship networks from 59 schools in the AddHealth study. Across this heterogeneous sample, the best-fitting models included qualitatively similar patterns of assortative mixing on individual attributes (sex, race, grade) and of triadic effects (a friend’s friend is a friend).