Skip to main content
SpringerLink
Log in

Multilevel Network Analysis Using ERGM and Its Extension

  • Chapter
  • First Online:
Book cover Multilevel Network Analysis for the Social Sciences

Part of the book series: Methodos Series ((METH,volume 12))

Abstract

Exponentials random graph models (ERGMs) model network structure as endogenous based on the assumption that network ties are conditionally dependent, i.e. the existence of a network tie depends on the existence of other network ties conditioning on the rest of the network. In multilevel network contexts, ERGMs offer a statistical framework that captures complicated multilevel structure through some simple structural signatures or network configurations based on these tie dependence assumptions, i.e. network ties are interdependent not only within levels but also across levels. The interpretations of ERGM parameters make hypothesis testing about multilevel network structure possible. In this chapter, we first review the multilevel network data structure and multilevel ERGM specifications. Then we will apply these models to a dataset collected among 265 farmers and their communication network in a rural community in Ethiopia, thus providing an interesting description of this farming community. The modelling example highlights the features of these models and their theoretical importance, i.e. within-level network structures are interdependent with network structures of other levels; and within level nodal attributes can affect multilevel network structures. For example, we extend the model specifications with two new configurations, the “Alternating” forms of cross-level three-paths and Four-cycles, and discus their possible interpretations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Since the model adequately fitted the statistics of education activity for entrepreneurial farmers, we can consider such effect is not significantly different from 0.

  2. 2.

    Besides under-fitting the interaction triangle effects (TriangleXBX and ATXBX), the model also under-fitted the bipartite clustering coefficient as the ratio between the number of four-cycles and three-paths (Robins and Alexander 2004), as suggested by the t-ratio of 2.04.

References

  • Agneessens, F., & Roose, H. (2008). Local structural properties and attribute characteristics in 2-mode networks: p* models to map choices of theater events. Journal of Mathematical Sociology, 32(3), 204–237.

    Article  Google Scholar 

  • Bewket, W. (2007). Soil and water conservation intervention with conventional technologies in northwestern highlands of Ethiopia: acceptance and adoption by farmers. Land Use Policy, 24(2), 404–416.

    Article  Google Scholar 

  • Bodin, Ö., & Tengö, M. (2012). Disentangling intangible social–ecological systems. Global Environmental Change, 22(2), 430–439.

    Article  Google Scholar 

  • Burt, R. S. (1976). Positions in networks. Social Forces, 55, 93–122.

    Article  Google Scholar 

  • Central Statistical Agency. (2004). The Federal Democratic Republic of Ethiopia statistical abstract for 2003. Addis Ababa: Central Statistical Agency.

    Google Scholar 

  • Deressa, T. T. (2007). Measuring the economic impact of the climate change on Ethiopian agriculture: Ricardian approach. Washington, DC: The World Bank.

    Book  Google Scholar 

  • Erdös, P., & Rényi, A. (1960). On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Science, 5, 17–61.

    Google Scholar 

  • Frank, O., & Strauss, D. (1986). Markov graphs. Journal of the American Statistical Association, 81(395), 832–842.

    Article  Google Scholar 

  • Handcock, M. S. (2003). In assessing degeneracy statistical models of social networks (Working Paper No. 39). Center for Statistics and the Social Sciences, University of Washington.

    Google Scholar 

  • Lazega, E., Jourda, M. T., Mounier, L., & Stofer, R. (2008). Catching up with big fish in the big pond? Multi-level network analysis through linked design. Social Networks, 30(2), 159–176.

    Article  Google Scholar 

  • Lorrain, F., & White, H. C. (1971). Structural equivalence of individuals in social networks. Journal of Mathematical Sociology, 1, 49–80.

    Article  Google Scholar 

  • Lusher, D., Koskinen, J., & Robins, G. (Eds.). (2013). Exponential random graph models for social networks: Theory, methods, and applications. New York: Cambridge University Press.

    Google Scholar 

  • Matous, P., & Todo, Y. (2015). Exploring dynamic mechanisms of learning networks for resource conservation. Ecology and Society, 20(2), 36.

    Article  Google Scholar 

  • Matous, P., Todo, Y., & Mojo, D. (2013a). Roles of extension and ethno-religious networks in acceptance of resource-conserving agriculture among Ethiopian farmers. International Journal of Agricultural Sustainability, 11(4), 301–316.

    Article  Google Scholar 

  • Matous, P., Todo, Y., & Mojo, D. (2013b). Boots are made for walking: Interactions across physical and social space in infrastructure-poor regions. Journal of Transport Geography, 31, 226–235.

    Article  Google Scholar 

  • Matous, P., Todo, Y., & Ishikawa, T. (2014). Emergence of multiplex mobile phone communication networks across rural areas: An Ethiopian experiment. Network Science, 2(02), 162–188.

    Article  Google Scholar 

  • Mojo, D., Todo, Y., & Matous, P. (2010). Perception of farmers and agricultural professionals on changes in productivity and water resources in Ethiopia. World Academy of Science, Engineering and Technology, 1(66), 860–868.

    Google Scholar 

  • Pattison, P., & Snijders, T. (2013). Modelling social networks: Next steps. In D. Lusher, J. Koskinen, & G. Robins (Eds.), Exponential random graph models for social networks, theory, methods, and applications (pp. 287–301). New York: Cambridge University Press.

    Google Scholar 

  • Rinaldo, A., Fienberg, S., & Zhou, Y. (2009). On the geometry of discrete exponential families with application to exponential random graph models. Electronic Journal of Statistics, 3, 446–484.

    Article  Google Scholar 

  • Robins, G., & Alexander, M. (2004). Small worlds among interlocking directors: Network structure and distance in bipartite graphs. Computational & Mathematical Organization Theory, 10(1), 69–94.

    Article  Google Scholar 

  • Robins, G., Elliott, P., & Pattison, P. (2001). Network models for social selection processes. Social Networks, 23(1), 1–30.

    Article  Google Scholar 

  • Robins, G., Pattison, P., Kalish, Y., & Lusher, D. (2007). An introduction to exponential random graph (p*) models for social networks. Social Networks, 29(2), 173–191.

    Article  Google Scholar 

  • Skvoretz, J., & Faust, K. (1999). Logit models for affiliation networks. Sociological Methodology, 29(1), 253–280.

    Article  Google Scholar 

  • Snijders, T. A. (2002). Markov chain Monte Carlo estimation of exponential random graph models. Journal of Social Structure, 3(2), 1–40.

    Google Scholar 

  • Snijders, T. A., Pattison, P. E., Robins, G. L., & Handcock, M. S. (2006). New specifications for exponential random graph models. Sociological Methodology, 36(1), 99–153.

    Article  Google Scholar 

  • Wang, P. (2013). Exponential random graph model extensions: Models for multiple networks and bipartite networks. In D. Lusher, J. Koskinen, & G. Robins (Eds.), Exponential random graph models for social networks: Theory, methods, and applications (pp. 115–129). New York: Cambridge University Press.

    Google Scholar 

  • Wang, P., Pattison, P., & Robins, G. (2009). PNet: A program for simulations and estimations of exponential random graph models. Melbourne school of psychological sciences, University of Melbourne, Australia. http://sna.unimelb.edu.au/PNet

  • Wang, P., Pattison, P., & Robins, G. (2013a). Exponential random graph model specifications for bipartite networks—A dependence hierarchy. Social Networks, 35(2), 211–222.

    Article  Google Scholar 

  • Wang, P., Robins, G., Pattison, P., & Lazega, E. (2013b). Exponential random graph models for multilevel networks. Social Networks, 35(1), 96–115.

    Article  Google Scholar 

  • Wang, P., Robins, G., Pattison, P., & Lazega, E. (2015). Social selection models for multilevel networks. Social Networks, 35, 96–115.

    Google Scholar 

  • Wasserman, S., & Iacobucci, D. (1991). Statistical modeling of one-mode and two-mode networks: Simultaneous analysis of graphs and bipartite graphs. British Journal of Mathematical and Statistical Psychology, 44, 13–44.

    Article  Google Scholar 

  • Wasserman, S., & Pattison, P. (1996). Logit models and logistic regressions for social networks: I. An introduction to Markov graphs and p*. Psychometrika, 61(3), 401–425.

    Article  Google Scholar 

  • Zappa, P., & Robins, G. (2015). Organizational learning across multi-level networks. Social Networks (in press).

    Google Scholar 

Download references

Acknowledgements

We thankfully acknowledge the ideas of Yoshihisa Kashima and the contribution of Yasuyuki Todo and Dagne Mojo in gathering of the data. The fieldwork was financially supported by the Ministry of Education, Culture, Sports, Science and Technology in Japan.

Author information

Authors and Affiliations

  1. Centre for Transformative Innovation, Faculty of Business and Law, Swinburne University of Technology, Hawthorn, VIC, Australia

    Peng Wang

  2. Melbourne School of Psychological Sciences, The University of Melbourne, Parkville, VIC, Australia

    Garry Robins

  3. School of Civil Engineering, Faculty of Engineering and Information Technologies, The University of Sydney, NSW, Australia

    Petr Matous

Authors
  1. Peng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Garry Robins
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Petr Matous
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peng Wang .

Editor information

Editors and Affiliations

  1. CSO-CNRS, Institut d’Etudes Politiques de Paris, SPC, Paris, France

    Emmanuel Lazega

  2. Nuffield College, University of Oxford, Oxford, United Kingdom

    Tom A.B. Snijders

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Wang, P., Robins, G., Matous, P. (2016). Multilevel Network Analysis Using ERGM and Its Extension. In: Lazega, E., Snijders, T. (eds) Multilevel Network Analysis for the Social Sciences. Methodos Series, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-24520-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24520-1_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24518-8

  • Online ISBN: 978-3-319-24520-1

  • eBook Packages: Social SciencesSocial Sciences (R0)

Publish with us

Policies and ethics

Search

Navigation