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A stochastic block model approach for the analysis of multilevel networks: An application to the sociology of organizations

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  • Chabert-Liddell, Saint-Clair
  • Barbillon, Pierre
  • Donnet, Sophie
  • Lazega, Emmanuel

Abstract

A multilevel network is defined as the junction of two interaction networks, one level representing the interactions between individuals and the other the interactions between organizations. The levels are linked by an affiliation relationship, each individual belonging to a unique organization. A new Stochastic Block Model is proposed as a unified probabilistic framework tailored for multilevel networks. This model contains latent blocks accounting for heterogeneity in the patterns of connection within each level and introducing dependencies between the levels. The sought connection patterns are not specified a priori which makes this approach flexible. Variational methods are used for the model inference and an Integrated Classified Likelihood criterion is developed for choosing the number of blocks and also for deciding whether the two levels are dependent or not. A comprehensive simulation study exhibits the benefit of considering this approach, illustrates the robustness of the clustering and highlights the reliability of the criterion used for model selection. This approach is applied on a sociological dataset collected during a television program trade fair, the inter-organizational level being the economic network between companies and the inter-individual level being the informal network between their representatives. It brings a synthetic representation of the two networks unraveling their intertwined structure and confirms the coopetition at stake.

Suggested Citation

  • Chabert-Liddell, Saint-Clair & Barbillon, Pierre & Donnet, Sophie & Lazega, Emmanuel, 2021. "A stochastic block model approach for the analysis of multilevel networks: An application to the sociology of organizations," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:csdana:v:158:y:2021:i:c:s016794732100013x
    DOI: 10.1016/j.csda.2021.107179
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    References listed on IDEAS

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    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
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    3. Pierre Barbillon & Sophie Donnet & Emmanuel Lazega & Avner Bar-Hen, 2017. "Stochastic block models for multiplex networks: an application to a multilevel network of researchers," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 295-314, January.
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    6. Julien Brailly, 2016. "Dynamics of networks in trade fairs—A multilevel relational approach to the cooperation among competitors," Journal of Economic Geography, Oxford University Press, vol. 16(6), pages 1279-1301.
    7. Bartolucci, Francesco & Marino, Maria Francesca & Pandolfi, Silvia, 2018. "Dealing with reciprocity in dynamic stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 86-100.
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    Cited by:

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    2. Fabio Ashtar Telarico & Franc Mali & Aleš Žiberna, 2024. "Revealing dynamic co-authorship structure in the social sciences through blockmodeling: the Slovenian case (1991–2020)," Scientometrics, Springer;Akadémiai Kiadó, vol. 129(9), pages 5635-5672, September.

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