Improving ERGM starting values using simulated annealing

Much of the theory of estimation for exponential family models, which include exponential-family random graph models (ERGMs) as a special case, is well-established and maximum likelihood estimates (MLEs) in particular enjoy many desirable properties. However, in the case of many ERGMs, direct calculation of MLEs is impossible and therefore methods for approximating MLEs and/or alternative estimation methods must be employed. Many MLE approximation algorithms require an alternative estimate as a starting point. The maximum pseudo-likelihood estimator (MPLE) is frequently taken as this starting point. Here, we discuss a potentially large class of such alternatives based on the fact that, unlike the MLE, the MPLE fails to satisfy the so-called “likelihood principle”. This means that different networks may have different MPLEs even if they have the same sufficient statistics. We exploit this fact here to search for improved starting values for approximation-based MLE methods. The method we propose has shown its merit in producing an MLE for a network dataset and model that had defied estimation using all other known methods.