Title: Regression of binary network data with exchangeable latent errors Show Chinese title

Title: 具有可交换潜在误差的二元网络数据回归

Abstract: 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. Show Chinese abstract

Abstract: 无向二元网络数据由行为者对之间的对称关系指示数组成。 此类数据的回归模型允许估计外生协变量对网络的影响以及未观察到的数据的预测。 理想情况下，回归参数的估计量应考虑网络中涉及相同行为者的内在关系依赖性。 为了考虑这些依赖性，研究者开发了许多潜在变量网络模型，然而，许多潜在变量网络模型的估计计算复杂度较高，并且不清楚哪种模型最适合用于推断。 我们提出了基于可交换性假设的Probit交换模型（PX模型），该假设在文献中的许多潜在变量网络模型中都很常见。 PX模型可以表示任何可交换网络模型的前两个矩。 我们利用EM算法获得PX模型的近似最大似然估计量，该估计量极其计算高效。 通过模拟研究，我们展示了所提出模型的回归系数估计相较于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，并表明所提出的估计器相对于潜在变量网络模型的估计器显著减少了运行时间，同时保持了预测性能。