Comparison Between Maximum Likelihood Estimation and Maximum Pseudo-Likelihood Estimation for Exponential Random Graph Models

• Activity Number: 356
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Xiaolin Yang*+ and Alessandro Rinaldo and Stephen Fienberg
• Companies: Carnegie Mellon University and Carnegie Mellon University and Carnegie Mellon University
• Keywords: Exponential Random Graph Models ; Maximum Likelihood Estimation ; Maximum Pseudo-likelihood Estimation ; Degeneracy

Abstract

Exponential Random Graph Models(ERGMs) are widely used for describing network data. As with other exponential family settings, the normalizing constant is rarely available in close form and its computation, which requires enumerating all possible graphs, makes the parameter estimation intractable for large networks. One way to deal with this problem is to approximate the likelihood function by a tractable function that is simpler to maximize, e.g., by using the method of pseudo-likelihood estimation suggested in the early network literature. In this paper, we compare maximum likelihood and maximum pseudo-likelihood estimation schemes with respect to existence and related degeneracy properties. We show that they differ in a number of important aspects.