A Probit Network Model with Arbitrary Dependence

Abstract

In this paper, we adopt a latent variable method to formulate a network model with arbitrarily dependent structure. We assume that the latent variables follow a multivariate normal distribution and a link between two nodes forms if the sum of the corresponding node parameters exceeds the latent variable. The dependent structure among edges is induced by the covariance matrix of the latent variables. The marginal distribution of an edge is a probit function. We refer this model to as the \emph{Probit Network Model}. We show that the moment estimator of the node parameter is consistent. To the best of our knowledge, this is the first time to derive consistency result in a single observed network with globally dependent structures. We extend the model to allow node covariate information.

arXiv comment16 pages

References in corpus (5)

• The statistical mechanics of networks
• A central limit theorem in the $\beta$-model for undirected random graphs with a diverging number of vertices
• Asymptotics in directed exponential random graph models with an increasing bi-degree sequence
• Maximum entropy distributions on graphs
• Asymptotic normality in the maximum entropy models on graphs with an increasing number of parameters

Cited by in corpus (1)

• A Unified Framework for Inference in Network Models with Degree Heterogeneity and Homophily