An Approximation Method for Improving Dynamic Network Model Fitting

Abstract

There has been a great deal of interest recently in the modeling and simulation of dynamic networks, that is, networks that change over time. One promising model is the separable temporal exponential-family random graph model (ERGM) of Krivitsky and Handcock, which treats the formation and dissolution of ties in parallel at each time step as independent ERGMs. However, the computational cost of fitting these models can be substantial, particularly for large, sparse networks. Fitting cross-sectional models for observations of a network at a single point in time, while still a nonnegligible computational burden, is much easier. This article examines model fitting when the available data consist of independent measures of cross-sectional network structure and the duration of relationships under the assumption of stationarity. We introduce a simple approximation to the dynamic parameters for sparse networks with relationships of moderate or long duration and show that the approximation method works best in precisely those cases where parameter estimation is most likely to fail—networks with very little change at each time step. We consider a variety of cases: Bernoulli formation and dissolution of ties, independent-tie formation and Bernoulli dissolution, independent-tie formation and dissolution, and dependent-tie formation models.

Key Words:

• Exponential random graph models (ERGMs)
• Markov chain Monte Carlo
• Separable temporal exponential random graph models (STERGMs)

ACKNOWLEDGMENTS

This work is supported by NIH grants R01–GM083603, R01–HD068395, and R01–AI083060. We are grateful to Martina Morris, Skye Bender-deMoll, and the rest of the University of Washington network modeling team for helpful discussions.