Statistical Models, Degeneracy and Inference for Social Networks
Mark S. Handcock, (University of Washington), firstname.lastname@example.org
The process of formulation and information encapsulated within social networks result in a form of "relational data". Relational data arise in many social science fields and graph models are a natural approach to representing the structure of these relations. We consider statistical and stochastic models for such graphs that can be used to represent the structural characteristics of the networks. In our applications, the nodes usually represent people, and the edges represent a specified relationship between the people. A commonly used model formulation was introduced by Frank and Strauss (1986) and derived from developments in spatial statistics (Besag 1974). These models allow for the potentially complex dependencies within relational data structures. To date, the use of graph models for networks has been limited by three interrelated factors: the complexity of realistic models, paucity of empirically relevant simulation studies, and a poor understanding of the properties of inferential methods. In this talk we discuss solutions to these limitations. We emphasize the important of likelihood-based inferential procedures and role of Markov Chain Monte Carlo (MCMC) algorithms for simulation and inference. A primary ongoing issue is the identification of classes of realistic and parsimonious models. In this regard show the unsuitability of some commonly promoted Markov models classes because they can result in degenerate probability distributions. We also consider the suitability and inference for classes of "power law" models that have been proposed for certain random graphs. The ideas are motivated and illustrated by the study of sexual relations networks with the objective of understanding the social determinants of HIV spread.