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.

社交网络的统计模型使研究人员能够研究复杂的社会现象，这些现象引起了观察到的社会行为者之间关系的模式，并获得了对社会纽带和行为者相互依存性的深刻理解。这项研究大部分集中在中型到大型社交群体中的社交网络上。迄今为止，尽管团队，家庭和个人网络中的网络数据很少，但社交网络统计模型（尤其是指数家庭随机图模型（ERGMS））的这些进步很少用于研究小型网络。在许多领域都很普遍 在本文中，我们将回顾小型网络的ERGM估计，并建议在可能的情况下使用穷举枚举。我们开发了一种R包，该包使用称为“ ergmito”的最大似然估计（MLE）来实现小型网络的合并ERGM的估计。基于评估MLE估计器属性的广泛模拟研究的结果，我们得出结论，与近似方法相比，直接MLE估计有许多好处，并且这为可用于建模社交网络的有价值的方法创新创造了机会与ERGM。