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Exponential-Family Random Graph Models for Multi-Layer Networks

Published online by Cambridge University Press:  01 January 2025

Pavel N. Krivitsky Open the ORCID record for Pavel N. Krivitsky [Opens in a new window] ,
Laura M. Koehly Open the ORCID record for Laura M. Koehly [Opens in a new window]  and
Christopher Steven Marcum Open the ORCID record for Christopher Steven Marcum [Opens in a new window]
Pavel N. Krivitsky*
Affiliation:
The University of New South Wales
Laura M. Koehly
Affiliation:
National Institutes of Health
*
Correspondence should be made to Pavel N. Krivitsky, School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia. Email: p.krivitsky@unsw.edu.au
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Abstract

Multi-layer networks arise when more than one type of relation is observed on a common set of actors. Modeling such networks within the exponential-family random graph (ERG) framework has been previously limited to special cases and, in particular, to dependence arising from just two layers. Extensions to ERGMs are introduced to address these limitations: Conway–Maxwell–Binomial distribution to model the marginal dependence among multiple layers; a “layer logic” language to translate familiar ERGM effects to substantively meaningful interactions of observed layers; and nondegenerate triadic and degree effects. The developments are demonstrated on two previously published datasets.

Keywords

ERGMmulti-layermulti-relationalmultiplexityConway–Maxwell–Binomial
Type
Theory and Methods
Information
Psychometrika , Volume 85 , Issue 3 , September 2020 , pp. 630 - 659
Copyright
Copyright © 2020 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-020-09720-7) contains supplementary material, which is available to authorized users.

We would like to thank Drs. Carter T. Butts and Gustavo Sudre for reviewing an early draft of this manuscript. This work utilized the computational resources of the University of Wollongong’s National Institute for Applied Statistics Research Australia (NIASRA) HPC cluster and the NIH HPC Biowulf cluster (http://hpc.nih.gov) and was supported by the National Human Genome Research Institute’s Intramural Research Program (ZIAHG200335 to Koehly). Krivitsky wishes to thank the University of Wollongong Faculty of Engineering and Information Sciences and the National Institute for Applied Statistics Research Australia (NIASRA) for funding the travel to facilitate this work. We would also like to thank Drs. Emmanuel Lazega and Christian Steglich for providing us with datasets used in this project.

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