Exponential Random Graph Models with Big Networks: Maximum Pseudolikelihood Estimation and the Parametric Bootstrap

• Activity Number: 240 - Computationally Intensive Methods for Estimation and Inference
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Christian Schmid* and Bruce Desmarais
• Companies: The Pennsylvania State University and The Pennsylvania State University
• Keywords: ERGM ; Networks ; Dynamic Networks ; Bootstrap

Abstract

With the growth of interest in network data across fields, the Exponential Random Graph Model (ERGM) has emerged as the leading approach to the statistical analysis of network data. ERGM parameter estimation requires the approximation of an intractable normalizing constant. Simulation methods represent the state-of-the-art approach to approximating the normalizing constant, leading to estimation by Monte Carlo maximum likelihood (MCMLE). MCMLE is accurate when a large sample of networks is used to approximate the normalizing constant. However, as the size of the network increases, MCMLE is computationally expensive, and may be prohibitively so if the size of the network is on the order of 10,000. When the network is large, one option for estimation is maximum pseudolikelihood (MPLE). MPLE is considerably less accurate than MLE in small networks, but exhibits comparable mean squared error in large networks. The standard MPLE is simple and fast, but generally underestimates standard errors. We show that a resampling method---the parametric bootstrap---results in accurate coverage probabilities for confidence intervals. Furthermore, bootstrapped MPLE is embarrassingly parallel.