Sociologický časopis / Czech Sociological Review 2024, 60(1): 7-35 | DOI: 10.13060/csr.2023.046

Exponential Random Graph Models: Modelling Relational Mechanisms in the Inter-organisational Network of the Czech Coal Subsystem

Tomáš Diviák ORCID...1, Petr Ocelík ORCID...2
1 Department of Criminology a Mitchell Centre for Social Network Analysis, University of Manchester
2 Fakulta sociálních studií, Masarykova univerzita, Brno

This study provides the first comprehensive introduction to exponential random graph models (ERGM) in the Czech academic literature. In it we apply ERGM to a network of 68 organisations involved in the Czech coal policy subsystem. First, we summarise the major limitations of the statistical modelling of network data arising from the interdependencies among observations and explain principled solutions to them provided by ERGM. Next, we discuss ERGM’s metatheoretical assumptions and their embeddedness within the broader context of social science research. We then introduce three types of relational mechanisms (endogenous, individual, and dyadic) operationalised as specific configurations, which we illustrate through the empirical example of an expert information network. Following a descriptive analysis we apply ERGM, breaking it down into three main steps: simulation, estimation, and estimation assessment. We provide a detailed interpretation of the model’s development and results, along with recommendations for building a model and solutions to convergence failure problems. One important finding is that one predictor of the exchange of expert information is ideological homophily, which reduces the potential of expertise to seek compromise solutions. We close with a discussion of the results and ERGM extensions to apply to more complex types of network data such as bipartite and multiplex networks and valued and longitudinal data.

Keywords: social network analysis, exponential random graph models, political networks, social mechanisms, statistical models

Received: May 20, 2022; Revised: August 15, 2023; Accepted: September 1, 2023; Prepublished online: September 19, 2023; Published: March 21, 2024  Show citation

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Diviák, T., & Ocelík, P. (2024). Exponential Random Graph Models: Modelling Relational Mechanisms in the Inter-organisational Network of the Czech Coal Subsystem. Sociologický časopis / Czech Sociological Review60(1), 7-35. doi: 10.13060/csr.2023.046
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References

  1. Amati, V. a Stadtfeld, C. (2021). Network Mechanisms and Network Models. In G. Manzo (ed.), Research Handbook on Analytical Sociology. Edward Elgar Publishing. https://doi.org/10.4337/9781789906851.00032 Go to original source...
  2. Block, P., Koskinen, J., Hollway, J., Steglich, C., a Stadtfeld, C. (2018). Change We Can Believe in: Comparing Longitudinal Network Models on Consistency, Interpretability and Predictive Power. Social Networks, 52, 180-191. https://doi.org/10.1016/j.socnet.2017.08.001 Go to original source...
  3. Brandes, U., Robins, G., McCranie, A. a Wasserman, S. (2013). What Is Network Science? Network Science, 1(01), 1-15. https://doi.org/10.1017/nws.2013.2 Go to original source...
  4. Coleman, J. S. (1988). Social Capital in the Creation of Human Capital. American Journal of Sociology, 94, S95-S120. https://doi.org/10.1086/228943 Go to original source...
  5. Cranmer, S. J., Desmarais, B. A., a Morgan, J. W. (2020). Inferential Network Analysis. Cambridge University Press. https://doi.org/10.1017/9781316662915 Go to original source...
  6. Daraganova, G., Pattison, P., Koskinen, J., Mitchell, B., Bill, A., Watts, M. a Baum, S. (2012). Networks and Geography: Modelling Community Network Structures as the Outcome of Both Spatial and Network Processes. Social Networks, 34(1), 6-17. https://doi.org/10.1016/j.socnet.2010.12.001 Go to original source...
  7. De Solla Price, D. (1976). A General Theory of Bibliometric and Other Cumulative Advantage Processes. Journal of the American Society for Information Science, 27(5), 292-306. https://doi.org/10.1002/asi.4630270505 Go to original source...
  8. Fischer, M. a Sciarini, P. (2015). Unpacking Reputational Power: Intended and Unintended Determinants of the Assessment of Actors' Power. Social Networks, 42, 60-71. https://doi.org/10.1016/j.socnet.2015.02.008 Go to original source...
  9. Hanneke, S., Fu, W., a Xing, E. P. (2010). Discrete Temporal Models of Social Networks. Electronic Journal of Statistics, 4, 585-605. https://doi.org/10.1214/09-EJS548 Go to original source...
  10. Harris, J. K. (2014). An Introduction to Exponential Random Graph Modeling. SAGE Publications Ltd. https://doi.org/10.4135/9781452270135 Go to original source...
  11. Hedström, P. (2005). Dissecting the Social: On the Principles of Analytical Sociology. Cambridge University Press. https://doi.org/10.1017/CBO9780511488801 Go to original source...
  12. Holland, P. W. a Leinhardt, S. (1971). Transitivity in Structural Models of Small Groups. Comparative Group Studies, 2(2), 107-124. https://doi.org/10.1177/104649647100200201 Go to original source...
  13. Kammerer, M., Wagner, P. M., Gronow, A., Ylä-Anttila, T., Fisher, D. R. a Sun-Jin, Y. (2021). What Explains Collaboration in High and Low Conflict Contexts? Comparing Climate Change Policy Networks in Four Countries. Policy Studies Journal, 49(4), 1065-1086. https://doi.org/10.1111/psj.12422 Go to original source...
  14. Krivitsky, P. N. (2012). Exponential-family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 6(0), 1100-1128. https://doi.org/10.1214/12-EJS696 Go to original source...
  15. Krivitsky, P. N. a Handcock, M. S. (2014). A Separable Model for Dynamic Networks. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(1), 29-46. https://doi.org/10.1111/rssb.12014 Go to original source...
  16. Krivitsky, P. N., Hunter, D. R., Morris, M. a Klumb, C. (2022). ergm 4: New features. arXiv:2106.04997 [stat]. http://arxiv.org/abs/2106.04997
  17. Leifeld, P. a Schneider, V. (2012). Information Exchange in Policy Networks: INFORMATION EXCHANGE IN POLICY NETWORKS. American Journal of Political Science, 56(3), 731-744. https://doi.org/10.1111/j.1540-5907.2011.00580.x Go to original source...
  18. Levy, M. (2016). gwdegree: Improving Interpretation of Geometrically-weighted Degree Estimates in Exponential Random Graph Models. Journal of Open Source Software, 1(3). https://doi.org/10.21105/joss.00036 Go to original source...
  19. Lusher, D., Koskinen, J. a Robins, G. (ed.). (2013). Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications. Cambridge University Press. https://doi.org/10.1017/CBO9780511894701 Go to original source...
  20. Lusher, D. a Robins, G. (2012). Formation of Social Network Structure. In D. Lusher, J. Koskinen a G. Robins (ed.), Exponential Random Graph Models for Social Networks (s. 16-28). Cambridge University Press. https://doi.org/10.1017/CBO9780511894701.004 Go to original source...
  21. McPherson, M., Smith-Lovin, L. a Cook, J. M. (2001). Birds of a Feather: Homophily in Social Networks. Annual Review of Sociology, 27, 415-444. https://doi.org/10.1146/annurev.soc.27.1.415 Go to original source...
  22. Merton, R. K. (1968). The Matthew Effect in Science: The Reward and Communication Systems of Science Are Considered. Science, 159(3810), 56-63. https://doi.org/10.1126/science.159.3810.56 Go to original source...
  23. Ocelík, P., Svobodová, K., Hendrychová, M., Lehotský, L., Everingham, J.-A., Ali, S. … Lechner, A. (2019). A Contested Transition Toward a Coal-free Future: Advocacy Coalitions and Coal Policy in the Czech Republic. Energy Research & Social Science, 58, 101283. https://doi.org/10.1016/j.erss.2019.101283 Go to original source...
  24. Ripley, R. M., Snijders, T. A. B., Boda, Z., Vörös, A. a Preciado, P. (2019). Manual for SIENA version 4.0 (version February 21, 2019). University of Oxford, Department of Statistics, Nuffield College. http://www.stats.ox.ac.uk/siena/
  25. Rivera, M. T., Soderstrom, S. B. a Uzzi, B. (2010). Dynamics of Dyads in Social Networks: Assortative, Relational, and Proximity Mechanisms. Annual Review of Sociology, 36(1), 91-115. https://doi.org/10.1146/annurev.soc.34.040507.134743 Go to original source...
  26. Robins, G. (2013). A Tutorial on Methods for the Modeling and Analysis of Social Network Data. Journal of Mathematical Psychology, 57(6), 261-274. https://doi.org/10.1016/j.jmp.2013.02.001 Go to original source...
  27. Robins, G. (2015). Doing Social Network Research. SAGE publications.
  28. Robins, G. a Lusher, D. (2012). Simplified Account of an Exponential Random Graph Model as a Statistical Model. In D. Lusher, J. Koskinen a G. Robins (ed.), Exponential Random Graph Models for Social Networks (s. 29-36). Cambridge University Press. https://doi.org/10.1017/CBO9780511894701.005 Go to original source...
  29. Robins, G., Pattison, P., Kalish, Y. a Lusher, D. (2007). An Introduction to Exponential Random Graph (p*) Models for Social Networks. Social Networks, 29(2), 173-191. https://doi.org/10.1016/j.socnet.2006.08.002 Go to original source...
  30. Robins, G., Pattison, P. a Wang, P. (2009). Closure, Connectivity and Degree Distributions: Exponential Random Graph (p*) Models for Directed Social Networks. Social Networks, 31(2), 105-117. https://doi.org/10.1016/j.socnet.2008.10.006 Go to original source...
  31. Scott, J. a Carrington, P. J. (2011). The SAGE Handbook of Social Network Analysis. SAGE.
  32. Snijders, T. A. B. (1996). Stochastic Actor-oriented Models for Network Change. Journal of Mathematical Sociology. http://www.tandfonline.com/doi/abs/10.1080/0022250X.1996.9990178 Go to original source...
  33. Snijders, T. A. B. (2002). Markov Chain Monte Carlo Estimation of Exponential Random Graph Models. Journal of Social Structure, 3.
  34. Snijders, T. A. B. (2011). Statistical Models for Social Networks. Annual Review of Sociology, 37(1), 131-153. https://doi.org/10.1146/annurev.soc.012809.102709 Go to original source...
  35. Snijders, T. A. B. (2013). Network Dynamics. In R. Wittek, T. A. B. Snijders a V. Nee (ed.), The Handbook of Rational Choice Social Research (s. 252-280). Stanford Social Sciences, an imprint of Stanford University Press. Go to original source...
  36. Snijders, T. A. B. a Koskinen, J. (2012). Simulation, Estimation, and Goodness of Fit. In D. Lusher, J. Koskinen a G. Robins (ed.), Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications (s. 141-166). Cambridge University Press. https://doi.org/10.1017/CBO9780511894701.014 Go to original source...
  37. Snijders, T. A. B., Pattison, P. E., Robins, G. L. a Handcock, M. S. (2006). New Specifications for Exponential Random Graph Models. Sociological Methodology, 36(1), 99-153. https://doi.org/10.1111/j.1467-9531.2006.00176.x Go to original source...
  38. Snijders, T. A. B., van de Bunt, G. G. a Steglich, C. E. G. (2010). Introduction to Stochastic Actor-based Models for Network Dynamics. Social Networks, 32(1), 44-60. https://doi.org/10.1016/j.socnet.2009.02.004 Go to original source...
  39. Stadtfeld, C. a Amati, V. (2021). Network Mechanisms and Network Models. In G. Manzo (ed.), Research Handbook on Analytical Sociology (s. 432-452). Edward Elgar Publishing. https://doi.org/10.4337/9781789906851.00032 Go to original source...
  40. Victor, J. N., Montgomery, A. H. a Lubell, M. (ed.). (2018). The Oxford Handbook of Political Networks. Oxford University Press.
  41. Wagner, P. M., Ylä-Anttila, T., Gronow, A., Ocelík, P., Schmidt, L. a Delicado, A. (2021). Information Exchange Networks at the Climate Science-policy Interface: Evidence from the Czech Republic, Finland, Ireland, and Portugal. Governance, 34(1), 211-228. https://doi.org/10.1111/gove.12484 Go to original source...
  42. Wang, P. (2013). Exponential Random Graph Model Extensions: Models for Multiple Networks and Bipartite Networks. In D. Lusher, J. Koskinen a G. Robins (ed.), Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications (s. 115-129). Cambridge University Press. https://doi.org/10.1017/CBO9780511894701.012 Go to original source...
  43. Wang, P., Pattison, P. a Robins, G. (2013). Exponential Random Graph Model Specifications for Bipartite Networks-A Dependence Hierarchy. Social Networks, 35(2), 211-222. https://doi.org/10.1016/j.socnet.2011.12.004 Go to original source...
  44. Wang, P., Robins, G. a Pattison, P. (2009). PNet: Program for the Simulation and Estimation of Exponential Random Graph (p*) Models. University of Melbourne. https://doi.org/10.1016/j.socnet.2008.08.002 Go to original source...
  45. Wang, P., Robins, G., Pattison, P. a Lazega, E. (2013). Exponential Random Graph Models for Multilevel Networks. Social Networks, 35(1), 96-115. https://doi.org/10.1016/j.socnet.2013.01.004 Go to original source...
  46. Wasserman, S. a Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge University Press. https://doi.org/10.1017/CBO9780511815478 Go to original source...
  47. Weible, C. M., Heikkila, T. a Pierce, J. (2018). Understanding Rationales for Collaboration in High-intensity Policy Conflicts. Journal of Public Policy, 38(1), 1-25. https://doi.org/10.1017/S0143814X16000301 Go to original source...