Stratified Proposal for MCMC Sampling in Exponential Random Graph Models (ERGMs)

• Activity Number: 542
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Junchi Guo* and Michael Larsen
• Companies: and The George Washington University
• Keywords: Tie-no-Tie (TNT) algorithm ; GWESP statistics ; transitivity effect ; Metropolis Hastings algorithm ; Social Network Analysis ; proposal distribution

Abstract

Exponential Random Graph Models (ERGMs) are one class of models used to describe observations from a social network. ERGMs have been used in many applications and are popular due to their ability to model transitivity of associations among other social network factors. Parameters of ERGMs are computationally intensive to estimate due to the need to use simulation to deal with the intractable normalizing constants. Metropolis Hastings (MH) algorithms randomly sample pairs of nodes in a network and flip the association between the pairs on or off. This is very inefficient due to the sparsity of typical networks. Current sampling methods improve on naive schemes by sampling pairs with different rates based on the current existence of edges between members of the pair. The novel proposal in this paper is to sample pairs with probabilities conditional on higher-order descriptions of the social network. This leads to a new proposal distribution for MH sampling for ERGMs. The innovation aims to solve a bad mixing problem when a transitivity effect is modeled in ERGMs. Methods are demonstrated on an application from the AddHealth study. Suggestions for future extensions are described.