Undirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models, however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the Probit Exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically-aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance.

翻译：无向二进制网络数据由参与者对之间对称关系的指标构成。此类数据的回归模型能够估计外生协变量对网络的影响，并预测未观测数据。理想情况下，回归参数的估计量应考虑网络中涉及同一参与者的关系之间固有的依赖性。为处理此类依赖性，研究者已开发了多种潜在变量网络模型，然而许多潜在变量网络模型的估计计算复杂，且难以确定何种模型最适合进行推断。我们提出了用于无向二进制网络数据的Probit可交换（PX）模型，该模型基于可交换性假设，这一假设普遍存在于文献中的许多潜在变量网络模型中。PX模型可表示任何可交换网络模型的前两阶矩。我们利用EM算法获得PX模型的近似极大似然估计量，该估计量计算效率极高。通过模拟研究，我们展示了所提模型在回归系数估计上较现有潜在变量网络模型的改进。在对政治倾向书籍购买行为的分析中，我们展示了购买行为中的政治极化现象，并证明所提估计量在保持预测性能的同时，相比潜在变量网络模型的估计量显著缩短了运行时间。