Profile least squares estimation in networks with covariates

TL;DR

This paper introduces a profile least squares method to estimate and analyze the influence of observed covariates and unobserved factors in network interactions, providing a simple algorithm and inference tools.

Contribution

It develops a novel estimation framework combining covariate effects and latent structure in networks using profile least squares, with a bootstrap inference procedure.

Findings

Effective estimation of covariate and residual effects in networks.

Bootstrap method enables inference on covariate significance.

Application to real datasets demonstrates practical usefulness.

Abstract

Many real world networks exhibit edge heterogeneity with different pairs of nodes interacting with different intensities. Further, nodes with similar attributes tend to interact more with each other. Thus, in the presence of observed node attributes (covariates), it is of interest to understand the extent to which these covariates explain interactions between pairs of nodes and to suitably estimate the remaining structure due to unobserved factors. For example, in the study of international relations, the extent to which country-pair specific attributes such as the number of material/verbal conflicts and volume of trade explain military alliances between different countries can lead to valuable insights. We study the model where pairwise edge probabilities are given by the sum of a linear edge covariate term and a residual term to model the remaining heterogeneity from unobserved factors. We approach estimation of the model via profile least squares and show how it leads to a simple algorithm to estimate the linear covariate term and the residual structure that is truly latent in the presence of observed covariates. Our framework lends itself naturally to a bootstrap procedure which is used to draw inference on model parameters, such as to determine significance of the homophily parameter or covariates in explaining the underlying network structure. Application to four real network datasets and comparisons using simulated data illustrate the usefulness of our approach.