Hostname: page-component-77f85d65b8-t6st2 Total loading time: 0 Render date: 2026-04-18T21:17:37.137Z Has data issue: false hasContentIssue false
  • English
  • Français

Inferential Network Analysis with Exponential Random Graph Models

Published online by Cambridge University Press:  04 January 2017

Skyler J. Cranmer  and
Bruce A. Desmarais
Skyler J. Cranmer*
Affiliation:
Department of Political Science, University of North Carolina at Chapel Hill, 311 Hamilton Hall, Chapel Hill, NC 27599
Bruce A. Desmarais
Affiliation:
Department of Political Science, University of Massachusetts Amherst, Thompson Hall, 200 Hicks Way, Amherst, MA 01003. e-mail: desmarais@polsci.umass.edu
*
e-mail: skyler@unc.edu (corresponding author)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Methods for descriptive network analysis have reached statistical maturity and general acceptance across the social sciences in recent years. However, methods for statistical inference with network data remain fledgling by comparison. We introduce and evaluate a general model for inference with network data, the Exponential Random Graph Model (ERGM) and several of its recent extensions. The ERGM simultaneously allows both inference on covariates and for arbitrarily complex network structures to be modeled. Our contributions are three-fold: beyond introducing the ERGM and discussing its limitations, we discuss extensions to the model that allow for the analysis of non-binary and longitudinally observed networks and show through applications that network-based inference can improve our understanding of political phenomena.

Information

Type
Research Article
Information
Political Analysis , Volume 19 , Issue 1 , Winter 2011 , pp. 66 - 86
Copyright
Copyright © The Author 2010. Published by Oxford University Press on behalf of the Society for Political Methodology 

Footnotes

Authors' note: Many thanks to Tom Carsey, James Fowler, Justin Gross, and Peter Mucha for their valuable comments on a previous version of this article. Supplementary materials for this article are available on the Political Analysis Web site.

References

Ahlquist, John Stephen, and Ward, Michael D. 2009. Factor endowments, trade, and democracy. Paper presented at the Annual Meeting of the Midwest Political Science Association, Chicago, IL.Google Scholar
Alvarez, R. Michael, and Nagler, Jonathan. 1998. When politics and models collide: estimating models of multiparty elections. American Journal of Political Science 42: 55–96.CrossRefGoogle Scholar
Baybeck, Brady, and Huckfeldt, Robert. 2002. Spatially dispersed ties among interdependent citizens: connecting individuals and aggregates. Political Analysis 10: 261–75.CrossRefGoogle Scholar
Besag, Julian. 1975. Statistical analysis of non-lattice data. Journal of the Royal Statistical Society. Series D (The Statistician) 24: 179–95.Google Scholar
Boehmke, Frederick J. 2006. The influence of unobserved factors on position timing and content in the NAFTA vote. Political Analysis 14: 421–38.CrossRefGoogle Scholar
Cao, Xun, Prakash, Aseem, and Ward, Michael D. 2007. Protecting jobs in the age of globalization: examining the relative salience of social welfare and industrial subsidies in OECD countries. International Studies Quarterly 51: 301–27.CrossRefGoogle Scholar
Crescenzi, Mark J. C. 2007. Reputation and interstate conflict. American Journal of Political Science 51: 382–96.CrossRefGoogle Scholar
Desmarais, Bruce A. 2010. Modeling interdependence in collective political decision making. PhD thesis University of North Carolina at Chapel Hill.Google Scholar
Desmarais, Bruce A., and Cranmer, Skyler J. 2010. Analyzing longitudinal networks: the temporal exponential random graph model In Midwest Political Science Association Annual Meeting, April 22, Chicago, IL.Google Scholar
Efron, Bradley. 1981. Nonparametric estimates of standard error: the jackknife, the bootstrap and other methods. Biometrika 68: 589–99.CrossRefGoogle Scholar
Faust, Katherine, and Skvoretz, John. 2002. Comparing networks across space and time, size and species. Sociological Methodology 32: 267–99.CrossRefGoogle Scholar
Fienberg, Stephen E., and Wasserman, Stanley S. 1981. Categorical data analysis of single sociometric relations. Sociological Methodology 12: 156–92.CrossRefGoogle Scholar
Fowler, James H. 2006. Connecting the Congress: A study of cosponsorship networks. Political Analysis 14: 456–87.CrossRefGoogle Scholar
Frank, Ove, and Strauss, David. 1986. Markov graphs. Journal of the American Statistical Association 81: 832–42.CrossRefGoogle Scholar
Franzese, Robert J. Jr., and Hays, Jude C. 2006. Strategic interaction among EU governments in active labor market policy-making: Subsidiarity and policy coordination under the European employment strategy. European Union Politics 7: 167–89.CrossRefGoogle Scholar
Franzese, Robert J. Jr., and Hays, Jude C. 2007. Spatial econometric models of cross-sectional interdependence in political science panel and time-series-cross-section data. Political Analysis 15: 140–64.CrossRefGoogle Scholar
Geyer, Charles J., and Thompson, Elizabeth A. 1992. Constrained Monte Carlo maximum likelihood for dependent data. Journal of the Royal Statistical Society. Series B (Methodological) 54: 657–99.CrossRefGoogle Scholar
Goodreau, Steven M., Kitts, James A., and Morris, Martina. 2009. Birds of a feather, or friend of a friend? Using exponential random graph models to investigate adolescent social networks. Demography 46: 103–25.CrossRefGoogle ScholarPubMed
Greene, William H. 2008. Econometric analysis. 6th ed. Upper Saddle River, NJ: Prentice Hall.Google Scholar
Handcock, Mark S. 2003. Assessing degeneracy in statistical models of social networks. Center for Statistics and the Social Sciences, University of Washington, Working Paper No. 39.Google Scholar
Handcock, Mark S., Hunter, David R., Butts, Carter T., Goodreau, Steven M., Morris, Martina, and Krivitsky, Pavel. 2010. ERGM: a package to fit, simulate and diagnose exponential-family models for networks. Version 2.2-2. Seattle, WA.Project home page at url http://statnetproject.org. http://CRAN.R-project.org/package=ergm Google Scholar
Handcock, Mark Stephen, and Gile, Krista Jennifer. 2010. Modeling networks from sampled data. Annals of Applied Statistics 4: 5–25.CrossRefGoogle ScholarPubMed
Hanneke, Steve, and Xing, Eric P. 2007. Discrete temporal models of social networks. In Statistical network analysis: Models, issues, and new directions. Vol. 4503 of Lecture Notes in Computer Science, 115–125. Berlin, Germany: Springer.Google Scholar
Hays, Jude C., Kachi, Aya, and Franzese, Robert J. Jr. 2010. A spatial model incorporating dynamic, endogenous network interdependence: A political science application. Statistical Methodology 7: 406–28.CrossRefGoogle Scholar
Hoag, Malcolm W. 1960. What interdependence for NATO? World Politics 12: 369–90.CrossRefGoogle Scholar
Hoff, Peter D., Raftery, Adrian E., and Handcock, Mark S. 2002. Latent space approaches to social network analysis. Journal of the American Statistical Association 97: 1090–8.CrossRefGoogle Scholar
Hoff, Peter D., and Ward, Michael D. 2004. Modeling dependencies in international relations networks. Political Analysis 12: 160–75.CrossRefGoogle Scholar
Holland, Paul W., and Leinhardt, Samuel. 1981. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association 76: 33–50.CrossRefGoogle Scholar
Hyvrinen, Aapo, Hurri, Jarmo, and Hoyer, Patrik O. 2009. Natural image statistics. London: Springer.CrossRefGoogle Scholar
Jackson, John E. 2002. A seemingly unrelated regression model for analyzing multiparty elections. Political Analysis 10: 49–65.CrossRefGoogle Scholar
Keohane, Robert O., and Nye, Joseph S. 1989. Power and interdependence. 2nd ed. Glenview, IL: Scott Foresman.Google Scholar
Kessler, Daniel, and Krehbiel, Keith. 1996. Dynamics of cosponsorship. The American Political Science Review 90: 555–66.CrossRefGoogle Scholar
King, Gary, Honaker, James, Joseph, Anne, and Scheve, Kenneth. 2001. Analyzing incomplete political science data: An alternative algorithm for multiple imputation. American Political Science Review 95: 49–69.CrossRefGoogle Scholar
Kroll, John A. 1993. The complexity of interdependence. International Studies Quarterly 37: 321–47.CrossRefGoogle Scholar
Lazer, David. 2005. Regulatory capitalism as a networked order: The international system as an informational network. Annals of the American Academy of Political and Social Science 598: 52–66.CrossRefGoogle Scholar
Lusher, Dean, and Ackland, Robert. 2010. A relational hyperlink analysis of an online social movement. Journal of Social Structure 11. http://www.cmu.edu/joss/content/articles/volume11/Lusher/.Google Scholar
Maoz, Zeev. 2006. Network polarization, network interdependence, and international conflict, 1816-2002. Journal of Peace Research 43: 391–411.CrossRefGoogle Scholar
Maoz, Zeev. 2009. The effects of strategic and economic interdependence on international conflict across levels of analysis. American Journal of Political Science 53: 223–40.CrossRefGoogle Scholar
Maoz, Zeev, and Russett, Bruce. 1993. Normative and structural causes of democratic peace, 1946-1986. The American Political Science Review 87: 624–38.CrossRefGoogle Scholar
Maoz, Zeev, Kuperman, Ranan D., Terris, Lesley, and Talmud, Ilan. 2006. Structural equivalence and international conflict: A social networks analysis. The Journal of Conflict Resolution 50: 664–89.CrossRefGoogle Scholar
Morris, Martina, Handcock, Mark S., and Hunter, David R. 2008. Specification of exponential-family random graph models: Terms and computational aspects. Journal of Statistical Software 24: 1–24.CrossRefGoogle ScholarPubMed
Park, Juyong, and Newman, M. E. J. 2004. Statistical mechanics of networks. Physical Review E 70: 66117–30.CrossRefGoogle ScholarPubMed
Pepe, Margaret Sullivan. 2000. An interpretation for the ROC curve and inference using GLM procedures. Biometrics 56: 352–9.CrossRefGoogle ScholarPubMed
Pete, Andras, Pattipati, Krishna R., and Kleinman, David L. 1993. Optimal team and individual decision rules in uncertain dichotomous situations. Public Choice 75: 205–30.CrossRefGoogle Scholar
Robins, Garry, Snijders, Tom, Wang, Peng, Handcock, Mark, and Pattison, Philippa. 2007. Recent developments in exponential random graph (p*) models for social networks. Social Networks 29: 192–215.CrossRefGoogle Scholar
Rosecrance, R., Alexandroff, A., Koehler, W., Kroll, J., Laqueur, S., and Stocker, J. 1977. Whither interdependence? International Organization 31: 425–71.CrossRefGoogle Scholar
Rosecrance, Richard, and Stein, Arthur. 1973. Interdependence: myth or reality. World Politics 26: 1–27.CrossRefGoogle Scholar
Saul, Zachary M., and Filkov, Vladimir. 2007. Exploring biological network structure using exponential random graph models. Bioinformatics 23: 2604–11.CrossRefGoogle ScholarPubMed
Schneider, Mark, Scholz, John, Lubell, Mark, Mindruta, Denisa, and Edwardsen, Matthew. 2003. Building consensual institutions: networks and the National Estuary Program. American Journal of Political Science 47: 143–58.CrossRefGoogle Scholar
Scholz, John T., and Wang, Cheng-Lung. 2006. Cooptation or transformation? Local policy networks and federal regulatory enforcement. American Journal of Political Science 50: 81–97.CrossRefGoogle Scholar
Snijders, T. A. B. 2002. Markov chain Monte Carlo estimation of exponential random graph models. Journal of Social Structure 3: 1–40.Google Scholar
Snijders, Tom A.B., van de Bunt, Gerhard G., and Steglich, Christian E. G. 2010. Introduction to stochastic actor-based models for network dynamics. Social Networks 32: 44–60.CrossRefGoogle Scholar
Snijders, Tom A.B., Pattison, Philippa E., Robins, Garry L., and Handcock, MarkS. 2006. New specifications for exponential random graph models. Sociological Methodology 36: 99–153.CrossRefGoogle Scholar
Strauss, David, and Ikeda, Michael. 1990. Pseudolikelihood estimation for social networks. Journal of the American Statistical Association 85: 204–12.CrossRefGoogle Scholar
van Duijn, Marijtje A.J., Gile, Krista J., and Handcock, Mark S. 2009. A framework for the comparison of maximum pseudolikelihood and maximum likelihood estimation of exponential family random graph models. Social Networks 31: 52–62.CrossRefGoogle ScholarPubMed
Ward, Michael D., and Hoff, Peter D. 2007. Persistent patterns of international commerce. Journal of Peace Research 44: 157–75.CrossRefGoogle Scholar
Ward, Michael D., Siverson, Randolph M., and Cao, Xun. 2007. Disputes, democracies, and dependencies: A re-examination of the Kantian Peace. American Journal of Political Science 51: 583–601.CrossRefGoogle Scholar
Wasserman, Stanley, and Pattison, Philippa. 1996. Logit models and logistic regressions for social networks: I. An introduction to Markov graphs and p*. Psychometrika 61: 401–25.CrossRefGoogle Scholar
Zhang, Yan, Friend, A. J., Traud, Amanda L., Porter, Mason A., Fowler, James H., and Mucha, Peter J. 2007. Community structure in Congressional cosponsorship networks. Physica A: Statistical Mechanics and Its Applications 387: 1705–12.Google Scholar
Supplementary material: PDF

Cranmer and Desmarais supplementary material

Appendix

Download Cranmer and Desmarais supplementary material(PDF)
PDF 188 KB