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Iterative estimation of mixed exponential random graph models with nodal random effects

Published online by Cambridge University Press:  25 January 2022

S. Kevork Open the ORCID record for S. Kevork [Opens in a new window]  and
G. Kauermann
S. Kevork*
Affiliation:
Institut für Statistik, Ludwig-Maximilians-Universität München, München, Germany.
G. Kauermann
Affiliation:
Institut für Statistik, Ludwig-Maximilians-Universität München, München, Germany.
*
*Corresponding author. Email: sevag.kevork@stat.uni-muenchen.de
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Abstract

The presence of unobserved node-specific heterogeneity in exponential random graph models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We, therefore, include node-specific random effects in the ERGM that account for unobserved heterogeneity in the network. This leads to a mixed model with parametric as well as random coefficients, labelled as mixed ERGM. Estimation is carried out by iterating between approximate pseudolikelihood estimation for the random effects and maximum likelihood estimation for the remaining parameters in the model. This approach provides a stable algorithm, which allows to fit nodal heterogeneity effects even for large scale networks. We also propose model selection based on the Akaike Information Criterion to check for node-specific heterogeneity.

Keywords

exponential random graph modelsrandom effectsgeneralized linear mixed modelsnetwork data analysis
Type
Research Article
Information
Network Science , Volume 9 , Issue 4 , December 2021 , pp. 478 - 498
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

Action Editor: Stanley Wasserman

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