Exponential random graph models for little networks

• Published in: Social networks Vol. 64; pp. 225 - 238
• Main Authors: Vega Yon, George G., Slaughter, Andrew, de la Haye, Kayla
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2021; Elsevier Science Ltd
• Subjects: Enumeration; Exact statistics; Exponential random graph models; Innovations; Maximum likelihood method; Simulation; Simulation study; Small networks; Social groups; Social networks; Teams; Exponential random graph models; Teams; Simulation study; Exact statistics; Small networks
• ISSN: 0378-8733; 1879-2111
• DOI: 10.1016/j.socnet.2020.07.005

•Methods for estimating ERGMs are centered around approximations.•Modern computers make it feasible to compute the ERGM support for small networks.•We wrote an R package (ergmito) that fits ERGMs for pooled models using MLE.•“Exact” methods can make big practical and inferential improvements.•Using “exact” methods opens a window for innovations in the little networks field. Statistical models for social networks have enabled researchers to study complex social phenomena that give rise to observed patterns of relationships among social actors and to gain a rich understanding of the interdependent nature of social ties and actors. Much of this research has focused on social networks within medium to large social groups. To date, these advances in statistical models for social networks, and in particular, of Exponential-Family Random Graph Models (ERGMS), have rarely been applied to the study of small networks, despite small network data in teams, families, and personal networks being common in many fields. In this paper, we revisit the estimation of ERGMs for small networks and propose using exhaustive enumeration when possible. We developed an R package that implements the estimation of pooled ERGMs for small networks using Maximum Likelihood Estimation (MLE), called “ergmito”. Based on the results of an extensive simulation study to assess the properties of the MLE estimator, we conclude that there are several benefits of direct MLE estimation compared to approximate methods and that this creates opportunities for valuable methodological innovations that can be applied to modeling social networks with ERGMs.