Improving Simulation-Based Algorithms for Fitting ERGMs

Markov chain Monte Carlo methods can be used to approximate the intractable normaliz-ing constants that arise in likelihood calculations for many exponential family random graph models for networks. However, in practice, the resulting approximations degrade as param-eter 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 net-work 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