Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models

TL;DR

This paper proposes a simple modification to ERGMs that adjusts for network size and composition effects, enabling more accurate modeling of social networks, especially with egocentric data, by preserving mean degree rather than density.

Contribution

It introduces an offset-based adjustment to ERGMs that accounts for network size and composition changes, improving their applicability to real-world social network data.

Findings

The adjustment preserves mean degree as networks grow.

The method enables ERGMs to handle egocentric sampling.

Application to NHSLS data demonstrates practical utility.

Abstract

Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without adjustment, ERGMs preserve density as network size increases. Density invariance is often not appropriate for social networks. We suggest a simple modification based on an offset which instead preserves the mean degree and accommodates changes in network composition asymptotically. We demonstrate that this approach allows ERGMs to be applied to the important situation of egocentrically sampled data. We analyze data from the National Health and Social Life Survey (NHSLS).