Fitting Social Network Models Using Varying Truncation Stochastic Approximation MCMC Algorithm

• Activity Number: 463
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Ick Hoon Jin*+
• Companies: Texas A & M University
• Keywords: Exponential Random Graph Model ; Stochastic Approximation Markov Chain Monte Carlo ; Model Degeneracy ; Trajectory Averaging ; Monte Carlo MLE ; Social Network

Abstract

The exponential random graph model (ERGM) plays a dominant role in social network analysis. However, the current methods, such as Monte Carlo MLE and stochastic approximation, often suffer from the model degeneracy problem in fitting ERGMs, rendering failures in parameter estimation. In this paper, we introduce a varying truncation stochastic approximation Markov chain Monte Carlo (SAMCMC) method for estimating the parameters of ERGMs. The varying truncation mechanism enables SAMCMC to overcome the model degeneracy problem. Under mild conditions, we show that the resulting estimator is consistent, asymptotically normal, and asymptotically efficient. The SAMCMC method is illustrated using a variety of social networks. The numerical results indicate that SAMCMC can significantly outperform the Monte Carlo MLE and stochastic approximation methods. For the ERGMs which consist of basic Markovian statistics, the Monte Carlo MLE and stochastic approximation methods often fail due to the model degeneracy, while SAMCMC still works well. For the ERGMs which do not suffer from the model degeneracy, SAMCMC can work equally well as or better than the pre-existing methods.