AbstractsMathematics

We address three aspects of statistical methodology in the application of Exponential family Random Graphs to modeling social network processes. The first is the topic of model degeneracy in ERGMs. We show this is a lack-of-fit problem  – a function of both the model specification and the observed data  – that can be diagnosed by exploiting the geometry of the model space. We propose new specifications based on nonlinear transformation of degenerate terms that are less vulnerable to degeneracy and retain the property of 'locality' needed for interpretation. The second chapter focuses on methodology for estimating partnership duration models in the context of social network dependence. We develop a statistical framework in which models with very different structures can be compared and evaluated. The third chapter presents a new ERGM-based framework for modeling the co-evolution of ties and vertex attributes (dynamic selection-influence models). The model extends the separable temporal ERGMs developed by Krivitsky (2009), with a flexible framework for representing hypothesized social mechanisms, and a corresponding likelihood-based inference framework. Advisors/Committee Members: Morris, Martina (advisor).