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.

网络往往以其节点异质性而著称，节点表现出不同程度的交互，以及节点同质性，即具有共同特征的节点倾向于相互关联。在本文中，我们严格研究了通过节点特定参数化捕捉前者的有向网络模型，并通过引入协变量来实现后者。具体而言，该模型通过不同的参数量化了每个节点的异质性程度，即其出度和入度，从而使得异质性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，并建立了所得到的估计量的均匀一致性和渐近正态性。数值研究验证了我们的理论发现，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。