• Corpus ID: 234723938

Regression of exchangeable relational arrays

@article{Marrs2017RegressionOE,
  title={Regression of exchangeable relational arrays},
  author={Frank W. Marrs and Bailey K. Fosdick and Tyler H. McCormick},
  journal={arXiv: Methodology},
  year={2017}
}

• Frank W. Marrs, B. Fosdick, T. McCormick
• Published 19 January 2017
• Mathematics
• arXiv: Methodology

Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Such data appear as trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms, and dynamic protein-protein interactions. Elements of a relational array are often modeled as a linear function of observable covariates, where the regression coefficients are the subjects of inference. The structure of the relational array engenders dependence among relations that involve the same actor. Uncertainty estimates for regression coefficient estimators -- and ideally the coefficient estimators themselves -- must account for this relational dependence. Existing estimators of standard errors that recognize such relational dependence rely on estimating extremely complex, heterogeneous structure across actors. This paper proposes a new class of parsimonious coefficient and standard error estimators for regressions of relational arrays. We leverage an exchangeability assumption to derive 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 network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression setting with relational data. We demonstrate improvements in inference theoretically, via a simulation study, and by analysis of a data set involving international trade.