Improving Simulation-Based Algorithms for Fitting ERGMs

Markov chain Monte Carlo methods can be used to approximate the intractable normalizing constants that arise in likelihood calculations for many exponential family random graph models for networks. However, in practice, the resulting approximations degrade as parameter values move away from the value used to define the Markov chain, even in cases where the chain produces perfectly efficient samples. We introduce a new approximation method along with a novel method of moving toward a maximum likelihood estimator (MLE) from an arbitrary starting parameter value in a series of steps based on alternating between the canonical exponential family parameterization and the mean-value parameterization. This technique enables us to find an approximate MLE in many cases where this was previously not possible. We illustrate these methods on a model for a transcriptional regulation network for E. coli, an example where previous attempts to approximate an MLE had failed, and a model for a well-known social network dataset involving friendships among workers in a tailor shop. These methods are implemented in the publicly available ergm package for R, and computer code to duplicate the results of this paper is included in the Supplemental Materials.