Relational arrays represent interactions or associations between pairs of actors, often in varied contexts or over time. Such data appear as, for example, trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms, and dynamic protein-protein interactions. In this talk, we propose and evaluate a new class of parameter standard errors for models that represent elements of a relational array as a linear function of observable covariates. Uncertainty estimates for regression coefficients must account for both heterogeneity across actors and dependence arising from relations involving the same actor. Existing estimators of parameter standard errors that recognize such 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 estimators in a variety of settings. This exchangeability assumption is pervasive in the network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression setting with relational data. We show that our estimator is consistent and demonstrate improvements in inference through simulation and a data set involving international trade.

Dr. Bailey Fosdick is an Assistant Professor in the Department of Statistics at Colorado State University. She earned her Ph.D. at the University of Washington in 2013 and spent a year as a Postdoctoral Fellow at the Statistical and Applied Mathematical Sciences Institute. Dr. Fosdick’s research primarily focuses on developing a methodology for the statistical analysis of social networks, motivated by pressing questions in population ecology, public health, political science, and sociology. Dr. Fosdick also works on methods for survey analysis and the analysis of multivariate data.