Inference for Network Regression Models with Community Structure

Mengjie Pan, Tyler McCormick, Bailey Fosdick

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 sci- ences. Valid inference relies on accurately model- ing 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 model- ing framework that models the errors as resulting from a community-based dependence structure and exploits the subsequent exchangeability prop- erties of the error distribution to obtain parsimo- nious standard errors for regression parameters.