Stochastic Weighted Graphs: Flexible Model Specification and Simulation

TL;DR

This paper introduces a flexible estimation method for the GERGM model of weighted networks, enabling broader application and improved modeling of network structures without degeneracy.

Contribution

We develop a Metropolis-Hastings algorithm that allows estimation of any GERGM specification, expanding the model's flexibility and applicability to various weighted network data.

Findings

New estimation method avoids likelihood degeneracy

Successfully applied to real network datasets

Simulated non-degenerate models demonstrating effectiveness

Abstract

In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The generalized exponential random graph model (GERGM) is a recently proposed method used to simulate and model the edges of a weighted graph. The GERGM specifies a joint distribution for an exponential family of graphs with continuous-valued edge weights. However, current estimation algorithms for the GERGM only allow inference on a restricted family of model specifications. To address this issue, we develop a Metropolis--Hastings method that can be used to estimate any GERGM specification, thereby significantly extending the family of weighted graphs that can be modeled with the GERGM. We show that new flexible model specifications are capable of avoiding likelihood degeneracy and efficiently capturing network structure in applications where such models were not previously available. We demonstrate the utility of this new class of GERGMs through application to two real network data sets, and we further assess the effectiveness of our proposed methodology by simulating non-degenerate model specifications from the well-studied two-stars model. A working R version of the GERGM code is available in the supplement and will be incorporated in the gergm CRAN package.