Degeneracy and Inference for Social Network Models

• Activity Number: 45
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Social Statistics Section*
• Author(s): Mark Handcock*+
• Affiliation(s): University of Washington
• Keywords: random graph models ; stochastic processes ; MCMC

Abstract

In this paper, we describe recent advances in the modeling of random graphs that have an impact on the representation of sexual and drug use networks. We also investigate issues related to the estimation of random graph models. The main focus is cross-sectional social network models, although dynamic or longitudinal models are briefly discussed.

To date, the use of stochastic graph models for networks has been limited by three interrelated factors: the complexity of realistic models, lack of use of simulation studies, and a poor understanding of the properties of inferential methods.

In this paper, we discuss these factors and related issues of the degeneracy of commonly promoted models. As a cornerstone of this development, we present a Markov Chain Monte Carlo (MCMC) algorithm for general random graph models. We also review the role of these MCMC algorithms for simulation, addressing model degeneracy, implementing Bayesian formulations and likelihood-based inference. These ideas are applied to a sexual relations network from Colorado Springs with the objective of understanding the social determinants of HIV spread.