# Regression of binary network data with exchangeable latent errors

Undirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of network regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for the inherent dependencies in network data, researchers have developed a host of latent variable network models, however, estimation of many latent variables models is computationally onerous, and which model is best to estimate or predict from may not be clear. We propose the Probit Exchangeable (PX) Model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the second moments of any exchangeable network model, yet specifies no particular parametric model. We propose an approximate maximum likelihood estimator for the PX model that allows for fast estimation. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models when generating from the PX model. In an analysis of purchases of politically-aligned books, we demonstrate political polarization in the network and show that the proposed model significantly reduces runtime relative to latent variable network models while maintaining predictive performance.

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