Regression of exchangeable relational arrays

作     者：Marrs, F. W. Fosdick, B. K. Mccormick, T. H. 

作者机构：Los Alamos Natl Lab Stat Sci POB 1663 Los Alamos NM 87545 USA Colorado State Univ Dept Stat 102 Stat Bldg Ft Collins CO 80523 USA Univ Washington Dept Stat Box 354322 Seattle WA 98195 USA 

出 版 物：《BIOMETRIKA》 (生物测量学)

年 卷 期：2023年第110卷第1期

页      面：265-272页

核心收录：

学科分类：0710[理学-生物学] 07[理学] 09[农学] 0714[理学-统计学（可授理学、经济学学位）] 

主　　题：Array data Dependent data Generalized least squares Weighted network 

摘      要：Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modelled as a linear function of observable covariates. Uncertainty estimates for regression coefficient estimators, and ideally the coefficient estimators themselves, must account for dependence between elements of the array, e.g., relations involving the same actor. Existing estimators of standard errors that recognize such relational dependence rely on estimating extremely complex, heterogeneous structure across actors. This paper develops 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 dataset involving international trade.