A Probit Network Model with Arbitrary Dependence

TL;DR

This paper introduces a Probit Network Model using latent variables with a multivariate normal distribution to capture arbitrary dependence among network edges, providing a new way to analyze complex dependent structures.

Contribution

It develops the first consistency proof for a single observed network with global dependence and extends the model to incorporate node covariates.

Findings

Moment estimator of node parameters is consistent.

Model captures arbitrary dependence via latent variable covariance.

Extension includes node covariate information.

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.