Statistical Models for Complete and Incomplete Network Data

Steven M. Goodreau, University of Washington
Laura M. Koehly, Texas A&M University
Martina Morris, University of Washington

There are two statistical approaches to modeling the structural regularities in networks of relations within a population. One, motivated by the interest in modeling the detailed dependence among ties, is based on exponential random graph models and requires complete network data. The other approach is motivated by the need to deal with the practical constraints of data collection, and is based on loglinear models that can be used with incomplete ("local network") data. We establish the link between these two modeling frameworks. Both are based on the exponential family, but use alternate forms of conditioning. In special cases the two probabilities are related via Bayes' rule and parameter values may be explicitly related. Understanding these links 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.