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Inferential Network Analysis with Exponential Random Graph Models

  • Skyler J. Cranmer (a1) and Bruce A. Desmarais (a2)

Abstract

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.

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Copyright

Corresponding author

e-mail: skyler@unc.edu (corresponding author)

Footnotes

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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.

Footnotes

References

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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.
Alvarez, R. Michael, and Nagler, Jonathan. 1998. When politics and models collide: estimating models of multiparty elections. American Journal of Political Science 42: 5596.
Baybeck, Brady, and Huckfeldt, Robert. 2002. Spatially dispersed ties among interdependent citizens: connecting individuals and aggregates. Political Analysis 10: 261–75.
Besag, Julian. 1975. Statistical analysis of non-lattice data. Journal of the Royal Statistical Society. Series D (The Statistician) 24: 179–95.
Boehmke, Frederick J. 2006. The influence of unobserved factors on position timing and content in the NAFTA vote. Political Analysis 14: 421–38.
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.
Crescenzi, Mark J. C. 2007. Reputation and interstate conflict. American Journal of Political Science 51: 382–96.
Desmarais, Bruce A. 2010. Modeling interdependence in collective political decision making. PhD thesis University of North Carolina at Chapel Hill.
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.
Efron, Bradley. 1981. Nonparametric estimates of standard error: the jackknife, the bootstrap and other methods. Biometrika 68: 589–99.
Faust, Katherine, and Skvoretz, John. 2002. Comparing networks across space and time, size and species. Sociological Methodology 32: 267–99.
Fienberg, Stephen E., and Wasserman, Stanley S. 1981. Categorical data analysis of single sociometric relations. Sociological Methodology 12: 156–92.
Fowler, James H. 2006. Connecting the Congress: A study of cosponsorship networks. Political Analysis 14: 456–87.
Frank, Ove, and Strauss, David. 1986. Markov graphs. Journal of the American Statistical Association 81: 832–42.
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.
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.
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.
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.
Greene, William H. 2008. Econometric analysis. 6th ed. Upper Saddle River, NJ: Prentice Hall.
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.
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
Handcock, Mark Stephen, and Gile, Krista Jennifer. 2010. Modeling networks from sampled data. Annals of Applied Statistics 4: 525.
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, 115125. Berlin, Germany: Springer.
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.
Hoag, Malcolm W. 1960. What interdependence for NATO? World Politics 12: 369–90.
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.
Hoff, Peter D., and Ward, Michael D. 2004. Modeling dependencies in international relations networks. Political Analysis 12: 160–75.
Holland, Paul W., and Leinhardt, Samuel. 1981. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association 76: 3350.
Hyvrinen, Aapo, Hurri, Jarmo, and Hoyer, Patrik O. 2009. Natural image statistics. London: Springer.
Jackson, John E. 2002. A seemingly unrelated regression model for analyzing multiparty elections. Political Analysis 10: 4965.
Keohane, Robert O., and Nye, Joseph S. 1989. Power and interdependence. 2nd ed. Glenview, IL: Scott Foresman.
Kessler, Daniel, and Krehbiel, Keith. 1996. Dynamics of cosponsorship. The American Political Science Review 90: 555–66.
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: 4969.
Kroll, John A. 1993. The complexity of interdependence. International Studies Quarterly 37: 321–47.
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: 5266.
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/.
Maoz, Zeev. 2006. Network polarization, network interdependence, and international conflict, 1816-2002. Journal of Peace Research 43: 391411.
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.
Maoz, Zeev, and Russett, Bruce. 1993. Normative and structural causes of democratic peace, 1946-1986. The American Political Science Review 87: 624–38.
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.
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: 124.
Park, Juyong, and Newman, M. E. J. 2004. Statistical mechanics of networks. Physical Review E 70: 66117–30.
Pepe, Margaret Sullivan. 2000. An interpretation for the ROC curve and inference using GLM procedures. Biometrics 56: 352–9.
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.
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: 192215.
Rosecrance, R., Alexandroff, A., Koehler, W., Kroll, J., Laqueur, S., and Stocker, J. 1977. Whither interdependence? International Organization 31: 425–71.
Rosecrance, Richard, and Stein, Arthur. 1973. Interdependence: myth or reality. World Politics 26: 127.
Saul, Zachary M., and Filkov, Vladimir. 2007. Exploring biological network structure using exponential random graph models. Bioinformatics 23: 2604–11.
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.
Scholz, John T., and Wang, Cheng-Lung. 2006. Cooptation or transformation? Local policy networks and federal regulatory enforcement. American Journal of Political Science 50: 8197.
Snijders, T. A. B. 2002. Markov chain Monte Carlo estimation of exponential random graph models. Journal of Social Structure 3: 140.
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: 4460.
Snijders, Tom A.B., Pattison, Philippa E., Robins, Garry L., and Handcock, MarkS. 2006. New specifications for exponential random graph models. Sociological Methodology 36: 99153.
Strauss, David, and Ikeda, Michael. 1990. Pseudolikelihood estimation for social networks. Journal of the American Statistical Association 85: 204–12.
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: 5262.
Ward, Michael D., and Hoff, Peter D. 2007. Persistent patterns of international commerce. Journal of Peace Research 44: 157–75.
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: 583601.
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.
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.
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Political Analysis
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