Iterative Estimation of Mixed Exponential Random Graph Models with Nodal Random Effects

TL;DR

This paper introduces a mixed ERGM with node-specific random effects to better model unobserved heterogeneity in networks, providing a stable estimation algorithm suitable for large networks.

Contribution

It extends ERGMs by incorporating random effects, developing an estimation method that combines penalized pseudolikelihood and maximum likelihood, and proposes an AIC-based model selection.

Findings

Stable estimation algorithm for large networks

Effective modeling of unobserved heterogeneity

AIC-based model selection for heterogeneity detection

Abstract

The presence of unobserved node specific heterogeneity in Exponential Random Graph Models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We therefore extend the ERGM by including node specific random effects that account for unobserved heterogeneity in the network. This leads to a mixed model with parametric as well as random coefficients, labelled as mixed ERGM. Estimation is carried out by combining approximate penalized pseudolikelihood estimation for the random effects with maximum likelihood estimation for the remaining parameters in the model. This approach provides a stable algorithm, which allows to fit nodal heterogeneity effects even for large scale networks. We also propose model selection based on the AIC to check for node specific heterogeneity.