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Friendship Networks Through Time: An Actor-Oriented Dynamic Statistical Network Model

Author

Listed:
  • Gerhard G. Van De Bunt

    (Vrije Universiteit Amsterdam, Faculty of Social-Cultural Sciences)

  • Marijtje A.J. Van Duijn

    (University of Groningen)

  • Tom A.B. Snijders

    (University of Groningen)

Abstract

We propose a class of actor-oriented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a data-set collected among university freshmen at 7 points in time during 1994 and 1995.

Suggested Citation

  • Gerhard G. Van De Bunt & Marijtje A.J. Van Duijn & Tom A.B. Snijders, 1999. "Friendship Networks Through Time: An Actor-Oriented Dynamic Statistical Network Model," Computational and Mathematical Organization Theory, Springer, vol. 5(2), pages 167-192, July.
    • Handle: RePEc:spr:comaot:v:5:y:1999:i:2:d:10.1023_a:1009683123448
    DOI: 10.1023/A:1009683123448
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    References listed on IDEAS

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    1. Stanley Wasserman & Dawn Iacobucci, 1988. "Sequential social network data," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 261-282, June.
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    Cited by:

    1. Dekker, D.J. & Franses, Ph.H.B.F. & Krackhardt, D., 2001. "An Equilibrium-Correction Model for Dynamic Network Data," ERIM Report Series Research in Management ERS-2001-39-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Shahadat Uddin & Arif Khan & Liaquat Hossain & Mahendra Piraveenan & Sven Carlsson, 2015. "A topological framework to explore longitudinal social networks," Computational and Mathematical Organization Theory, Springer, vol. 21(1), pages 48-68, March.
    3. Siegwart Lindenberg, 2000. "It Takes Both Trust and Lack of Mistrust: The Workings of Cooperation and Relational Signaling in Contractual Relationships," Journal of Management & Governance, Springer;Accademia Italiana di Economia Aziendale (AIDEA), vol. 4(1), pages 11-33, March.
    4. Joshua Lospinoso & Michael Schweinberger & Tom Snijders & Ruth Ripley, 2011. "Assessing and accounting for time heterogeneity in stochastic actor oriented models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(2), pages 147-176, July.
    5. Pink, Sebastian & Kretschmer, David & Leszczensky, Lars, 2020. "Choice modelling in social networks using stochastic actor-oriented models," Journal of choice modelling, Elsevier, vol. 34(C).
    6. Long, Emily & Gardani, Maria & McCann, Mark & Sweeting, Helen & Tranmer, Mark & Moore, Laurence, 2020. "Mental health disorders and adolescent peer relationships," Social Science & Medicine, Elsevier, vol. 253(C).
    7. Mercken, Liesbeth & Snijders, Tom A.B. & Steglich, Christian & de Vries, Hein, 2009. "Dynamics of adolescent friendship networks and smoking behavior: Social network analyses in six European countries," Social Science & Medicine, Elsevier, vol. 69(10), pages 1506-1514, November.
    8. Neil Hwang & Jiarui Xu & Shirshendu Chatterjee & Sharmodeep Bhattacharyya, 2022. "The Bethe Hessian and Information Theoretic Approaches for Online Change-Point Detection in Network Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 283-320, June.
    9. Buchmann, Tobias & Hain, Daniel & Kudic, Muhamed & Müller, Matthias, 2014. "Exploring the Evolution of Innovation Networks in Science-driven and Scale-intensive Industries: New Evidence from a Stochastic Actor-based Approach," IWH Discussion Papers 1/2014, Halle Institute for Economic Research (IWH).
    10. Mary-Anne Holfve-Sabel, 2015. "Students’ Individual Choices of Peers to Work with During Lessons May Counteract Segregation," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 122(2), pages 577-594, June.
    11. Sofia Dokuka & Diliara Valeeva, 2015. "Statistical Models for Analysis of Social Network Dynamics in Educational Studies," Voprosy obrazovaniya / Educational Studies Moscow, National Research University Higher School of Economics, issue 1, pages 201-213.
    12. Schweinberger, Michael & Snijders, Tom A.B., 2007. "Markov models for digraph panel data: Monte Carlo-based derivative estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4465-4483, May.
    13. Prasanta Bhattacharya & Tuan Q. Phan & Xue Bai & Edoardo M. Airoldi, 2019. "A Coevolution Model of Network Structure and User Behavior: The Case of Content Generation in Online Social Networks," Service Science, INFORMS, vol. 30(1), pages 117-132, March.
    14. Devari, Aashwinikumar & Nikolaev, Alexander G. & He, Qing, 2017. "Crowdsourcing the last mile delivery of online orders by exploiting the social networks of retail store customers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 105(C), pages 105-122.
    15. Mark Huisman & Tom A. B. Snijders, 2003. "Statistical Analysis of Longitudinal Network Data With Changing Composition," Sociological Methods & Research, , vol. 32(2), pages 253-287, November.
    16. Karen Haandrikman & Leo J. G. Wissen, 2012. "Explaining the Flight of Cupid’s Arrow: A Spatial Random Utility Model of Partner Choice," European Journal of Population, Springer;European Association for Population Studies, vol. 28(4), pages 417-439, November.
    17. Maurits C. de Klepper & Giuseppe (Joe) Labianca & Ed Sleebos & Filip Agneessens, 2017. "Sociometric Status and Peer Control Attempts: A Multiple Status Hierarchies Approach," Journal of Management Studies, Wiley Blackwell, vol. 54(1), pages 1-31, January.
    18. Hideki Fujiyama, 2020. "Network centrality, social loops, and utility maximization," Evolutionary and Institutional Economics Review, Springer, vol. 17(1), pages 39-70, January.

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