Statistical Inference in a Directed Network Model With Covariates

Ting Yan, Binyan Jiang, Stephen E. Fienberg, Chenlei Leng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

28 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)857-868
Number of pages12
JournalJournal of the American Statistical Association
Issue number526
Publication statusPublished - 11 Jul 2018


  • Asymptotic normality
  • Consistency
  • Degree heterogeneity
  • Homophily
  • Increasing number of parameters
  • Maximum likelihood estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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