Inference for Network Regression Models with Community Structure

TL;DR

This paper introduces a new network regression framework that models error dependencies based on community structures, improving inference accuracy by accounting for actor clustering.

Contribution

It proposes a community-based error dependence model that leverages exchangeability to produce more reliable standard errors for regression analysis in networks.

Findings

Enhanced modeling of residual dependencies in network data

More accurate standard errors for regression parameters

Applicable to social and biological network studies

Abstract

Network regression models, where the outcome comprises the valued edge in a network and the predictors are actor or dyad-level covariates, are used extensively in the social and biological sciences. Valid inference relies on accurately modeling the residual dependencies among the relations. Frequently homogeneity assumptions are placed on the errors which are commonly incorrect and ignore critical, natural clustering of the actors. In this work, we present a novel regression modeling framework that models the errors as resulting from a community-based dependence structure and exploits the subsequent exchangeability properties of the error distribution to obtain parsimonious standard errors for regression parameters.