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Bayesian exponential random graph models with nodal random effects
Institution:1. Institut für Statistik, Ludwigs-Maximilians-Universität München, Germany;2. School of Mathematics and Statistics and Insight: The National Centre for Data Analytics, University College Dublin, Ireland;3. School of Mathematical Sciences, Dublin Institute of Technology, Ireland;1. Wirtschafts-und Sozialwissenschaftliche Fakultät, Hector-Institut für Empirische Bildungsforschung, Universität Tübingen, Europastraße 6, 72072 Tübingen, Germany;2. Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstraße 7, 64289 Darmstadt, Germany;3. Department of Computer Science and Software Engineering, Concordia University, 1455, boul. de Maisonneuve ouest, Montréal, Québec, Canada H3G 1M8;1. Department of Biostatistics, University of Iowa, 145 N. Riverside Dr., Iowa City, IA 52242, USA;2. Department of Statistics, University of Illinois at Urbana-Champaign, 725 S. Wright Street, Champaign, IL 61820, USA;1. Department of Sociology, University of Notre Dame, United States;2. Departments of Sociology and Statistics, University of California, Irvine, United States;3. Departments of Criminology, Law and Society, and Sociology, University of California, Irvine, United States;4. Department of Psychology and Social Behavior, University of California, Irvine, United States;5. Program in Public Health, University of California, Irvine, United States;1. London School of Economics & Political Science, Department of Methodology, United Kingdom;2. University of Cambridge, Department of Sociology, United Kingdom
Abstract:We extend the well-known and widely used exponential random graph model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011) yields the basis of our modelling algorithm. A central question in network models is the question of model selection and following the Bayesian paradigm we focus on estimating Bayes factors. To do so we develop an approximate but feasible calculation of the Bayes factor which allows one to pursue model selection. Three data examples and a small simulation study illustrate our mixed model approach and the corresponding model selection.
Keywords:Exponential random graph models  Bayesian inference  Random effects  Network analysis
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