Some New Models for Social Networks

Abstract

Exponential-family Random Graph Models (ERGMs) have long been at the forefront of the analysis of relational data. The exponential-family form allows complex network dependencies to be represented. Models in this class are interpretable, flexible and have a strong theoretical foundation. The availability of powerful user-friendly open-source software allows broad accessibility and use. However, ERGMs sometimes suffer from a serious condition known as near-degeneracy, in which the model exhibits unrealistic probabilistic behavior or a severe lack-of-fit to real network data.

As such we need new models that build on the ERGM class while expanding their range. In this talk I will consider three such classes of models. The first is the Tapered ERGM class, which circumvents the issue of near-degeneracy while maintaining the desirable features of ERGMs. The second is the class of Exponential-family random network models (ERNM) that are capable of specifying a joint statistical representation of both the ties of a network and individual attributes. This class of models allow the nodal attributes to be modeled as stochastic processes, expanding the range and realism of exponential-family approaches to network modeling. The third is the Latent Order Logistic (LOLOG) model class that is based on a latent dynamic network formation process. Each of these classes is due to work by Ian E. Fellows. As one application of these classes, I will show how the ERNM class leads to a model for causality in a networked population when the underlying network is endogenous.

This is joint work with Ian E. Fellows, Bart Blackburn and Duncan A. Clark.