A MIXED EFFECTS MODEL FOR LONGITUDINAL RELATIONAL AND NETWORK DATA, WITH APPLICATIONS TO INTERNATIONAL TRADE AND CONFLICT

• Published in: The annals of applied statistics Vol. 5; no. 2A; pp. 843 - 872
• Main Authors: Westveld, Anton H., Hoff, Peter D.
• Format: Journal Article
• Language: English
• Published: Cleveland, OH Institute of Mathematical Statistics 01-06-2011; The Institute of Mathematical Statistics
• Subjects: Applications; Bayesian inference; Biology, psychology, social sciences; Data models; Exact sciences and technology; General topics; Gravity models; Imports; International trade; longitudinal data; Markov chains; Mathematics; militarized interstate disputes; Modeling; Musical intervals; network data; Parametric models; Polities; Probability and statistics; relational data; Sciences and techniques of general use; Social interaction; Statistics; Continuous set; Statistical method; Stochastic model; Mixed model; Binary response; Random effect; Psychometrics; Covariance matrix; Stochastic process
• ISSN: 1932-6157; 1941-7330
• DOI: 10.1214/10-AOAS403

The focus of this paper is an approach to the modeling of longitudinal social network or relational data. Such data arise from measurements on pairs of objects or actors made at regular temporal intervals, resulting in a social network for each point in time. In this article we represent the network and temporal dependencies with a random effects model, resulting in a stochastic process defined by a set of stationary covariance matrices. Our approach builds upon the social relations models of Warner, Kenny and Stoto [Journal of Personality and Social Psychology 37 (1979) 1742-1757] and Gill and Swartz [Canad. J. Statist. 29 (2001) 321-331] and allows for an intra- and inter-temporal representation of network structures. We apply the methodology to two longitudinal data sets: international trade (continuous response) and militarized interstate disputes (binary response).