Linking Random Graph and Loglinear Models of Networks

Many of the recent statistical models for the analysis of dependence in social networks build on the general class of exponential random graphs, including Markov random graphs, "p-star" models, and actor-oriented models.b In this talk we will examine how this class of models is related to the log-linear modeling framework used in earlier work to analyze mixing patterns in local network data.b Both approaches are based on the exponential family; random graphs model the probability that two actors form a partnership given their attributes and the rest of the data, while log-linear approaches model the probability that two actors have specific attributes given that they form a partnership. Under saturated tie independence models the two probabilities are related via Bayes rule, and parameter values may be explicitly related. For unsaturated models, the two frameworks do not contain equivalent models, and the underlying differences reveal assumptions about social behavior within the two frameworks.b It can be shown, however, that the two are expected to yield approximately equal fitted values in most practical applications.b Understanding the relationship between the two modeling classes sheds light on the relationship between local and complete network data, and the role that models can play in bridging the traditional gap between them.