Standard errors for regression on relational data with exchangeable errors

Relational arrays represent interactions or associations between pairs of actors, often over time or in varied contexts. We focus on the case where the elements of a relational array are modeled as a linear function of observable covariates. Due to the inherent dependencies among relations involving the same individual, standard regression methods for quantifying uncertainty in the regression coefficients for independent data are invalid. Existing estimators of coefficient standard errors that recognize relational dependence rely on estimating extremely complex, heterogeneous structure across actors. Leveraging an exchangeability assumption, we derive parsimonious standard error estimators that pool information across actors and are substantially more accurate than existing relational estimators in a variety of settings. This exchangeability assumption is pervasive in network and array models in the statistics literature, but not typically considered when adjusting for dependence in network regressions. We demonstrate the improvements in inference that result from using our proposed estimator through simulation and a dataset involving international trade.