Statistical Inference in a Directed Network Model With Covariates

Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this article, we rigorously study a directed network model that captures the former via node-specific parameterization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each node by different parameters, thus allowing the number of heterogeneity parameters to be twice the number of nodes. We study the maximum likelihood estimation of the model and establish the uniform consistency and asymptotic normality of the resulting estimators. Numerical studies demonstrate our theoretical findings and two data analyses confirm the usefulness of our model. Supplementary materials for this article are available online.

网络通常被定义为节点异质性的表征，其中节点表现出不同程度的交互作用，以及链接的同质性，即共享共同特征的节点倾向于相互关联。在本文中，我们严谨地研究了一种有向网络模型，该模型通过节点特定的参数化捕捉前者，并通过纳入协变量来体现后者。具体而言，该模型通过不同的参数量化了每个节点的异质程度，包括其出度和入度，从而使得异质参数的数量是节点数量的两倍。我们研究了该模型的最大似然估计，并建立了所得估计量的一致性和渐近正态性。数值研究证明了我们的理论发现，两次数据分析证实了我们的模型的有用性。本文的补充材料可在网上获取。