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Licensed Unlicensed Requires Authentication Published by De Gruyter May 11, 2017

Measurement Error and Attenuation Bias in Exponential Random Graph Models

  • Yeaji Kim , Leonardo Antenangeli and Justin Kirkland EMAIL logo

Abstract

Exponential Random Graph Models (ERGMs) are becoming increasingly popular tools for estimating the properties of social networks across the social sciences. While the asymptotic properties of ERGMs are well understood, much less is known about how ERGMs perform in the face of violations of the assumptions that drive those asymptotic properties. Given that empirical social networks rarely meet the strenuous assumptions of the ERGM perfectly, practical researchers are often in the position of knowing their coefficients are imperfect, but not knowing precisely how wrong those coefficients may be. In this research, we examine one violation of the asymptotic assumptions of ERGMs – perfectly measured social networks. Using several Monte Carlo simulations, we demonstrate that even randomly distributed measurement errors in networks under study can cause considerable attenuation in coefficients from ERGMs, and do real harm to subsequent hypothesis tests.

References

Alemán, Eduardo and Ernesto Calvo (2013) “Explaining Policy Ties in Presidential Congresses: A Network Analysis of Bill Initiation Data,” Political Studies, 61(2):356–377.10.1111/j.1467-9248.2012.00964.xSearch in Google Scholar

Aronow, Peter M. Cyrus Samii, and Valentina A. Assenova (2015) “Cluster–Robust Variance Estimation for Dyadic Data,” Political Analysis, 23(4):564–577.10.1093/pan/mpv018Search in Google Scholar

Baybeck, Brady, William D. Berry, and David A. Siegel (2011) “A Strategic Theory of Policy Diffusion via Intergovernmental Competition,” The Journal of Politics, 73(01):232–247.10.1017/S0022381610000988Search in Google Scholar

Berry, William D. and Brady Baybeck (2005) “Using Geographic Information Systems to Study Interstate Competition,” American Political Science Review, 99(04):505–519.10.1017/S0003055405051841Search in Google Scholar

Boehmke, Frederick J. and Paul Skinner (2012) “State Policy Innovativeness Revisited,” State Politics & Policy Quarterly, 20(10):1–27.10.1177/1532440012438890Search in Google Scholar

Box-Steffensmeier, Janet M. and Dino P. Christenson (2014) “The Evolution and Formation of Amicus Curiae Networks,” Social Networks, 36:82–96.10.1016/j.socnet.2012.07.003Search in Google Scholar

Box-Steffensmeier, Janet M., Dino P. Christenson and Matthew P. Hitt (2013) “Quality over Quantity: Amici Influence and Judicial Decision Making,” American Political Science Review, 107(03):446–460.10.1017/S000305541300021XSearch in Google Scholar

Cao, Xun (2012) “Global Networks and Domestic Policy Convergence: A Network Explanation of Policy Changes,” World Politics, 64(03):375–425.10.1017/S0043887112000081Search in Google Scholar

Carroll, Raymond J., Kathryn Roeder and Larry Wasserman (1999) “Flexible Parametric Measurement Error Models.” Biometrics, 55(1):44–54.10.1111/j.0006-341X.1999.00044.xSearch in Google Scholar

Cranmer, Skyler J. and Bruce A. Desmarais (2011) “Inferential Network Analysis with Exponential Random Graph Models,” Political Analysis, 19(1):66–86.10.1093/pan/mpq037Search in Google Scholar

Cranmer, Skyler J., Bruce A. Desmarais and Elizabeth J. Menninga (2012) “Complex Dependencies in the Alliance Network,” Conflict Management and Peace Science, 29(3):279–313.10.1177/0738894212443446Search in Google Scholar

Desmarais, Bruce A. and Skyler J. Cranmer (2013) “Forecasting the Locational Dynamics of Transnational Terrorism: A Network Analytic Approach,” Security Informatics, 2(1):1–12.10.1109/EISIC.2011.44Search in Google Scholar

Desmarais, Bruce A., Jeffrey J. Harden and Frederick J. Boehmke (2015) “Persistent Policy Pathways: Inferring Diffusion Networks in the American States,” American Political Science Review, 109(2):392–406.10.1017/S0003055415000040Search in Google Scholar

Dowdle, Andrew J. and Song Yang (2014) Why and Where the Money Flows: An ERGM Analysis of Shared Donors Among Presidential Candidates. Annual Meeting of the American Political Science Association.Search in Google Scholar

Erikson, Robert S., Pablo M. Pinto and Kelly T. Rader (2014) “Dyadic Analysis in International Relations: A Cautionary Tale.” Political Analysis, 22(4):457–463.10.1093/pan/mpt051Search in Google Scholar

Fowler, James H., Michael T. Heaney, David W. Nickerson, John F. Padgett and Betsy Sinclair (2011) “Causality in Political Networks.” American Politics Research, 39(2):437–480.10.1177/1532673X10396310Search in Google Scholar

Gomez-Rodriguez, Manuel, Jure Leskovec and Andreas Krause (2010) Inferring Networks of Diffusion and Influence. In KDD ’10: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery in Data Mining.10.1145/1835804.1835933Search in Google Scholar

Goodreau, Steven M., James A. Kitts and Martina Morris (2009) “Birds of a Feather, Or Friend of a Friend?: Using Exponential Random Graph Models to Investigate Adolescent Social Networks,” Demography, 46(1):103–125.10.1353/dem.0.0045Search in Google Scholar

Grossback, Lawrence J., Sean Nicholson-Crotty and David A. M. Peterson (2004) “Ideology and Learning in Policy Diffusion,” American Politics Research, 32(5):521–545.10.1177/1532673X04263801Search in Google Scholar

Guolo, Annamaria (2007) “Robust Techniques for Measurement Error Correction: A Review,” Statistical Methods in Medical Research, 17(6):555–580.10.1177/0962280207081318Search in Google Scholar

Handcock, Mark S., David R. Hunter, Carter T. Butts, Steven M. Goodreau and Martina Morris (2008) “Statnet: Software Tools for the Representation, Visualization, Analysis and Simulation of Network Data,” Journal of Statistical Software, 24(1):1548.10.18637/jss.v024.i01Search in Google Scholar

Heaney, Michael T. (2014) “Multiplex Networks and Interest Group Influence Reputation: An Exponential Random Graph Model,” Social Networks, 36:66–81.10.1016/j.socnet.2012.11.003Search in Google Scholar

Hoff, Peter D., Adrian E. Raftery and Mark S. Handcock (2002) “Latent space approaches to social network analysis,” Journal of the american Statistical association, 97(460): 1090–1098.10.21236/ADA458734Search in Google Scholar

Kinne, Brandon J. (2014) “Dependent Diplomacy: Signaling, Strategy, and Prestige in the Diplomatic Network,” International Studies Quarterly, 58(2):247–259.10.1111/isqu.12047Search in Google Scholar

Kirkland, Justin H. (2014) “Ideological Heterogeneity and Legislative Polarization in the United States,” Political Research Quarterly, 67(4). p. 1065912914532837.10.1177/1065912914532837Search in Google Scholar

Kirkland, Justin H. R. and Lucas Williams (2014) “Partisanship and Reciprocity in Cross-Chamber Legislative Interactions,” The Journal of Politics, 76(03):754–769.10.1017/S0022381614000097Search in Google Scholar

Koskinen, Johan and Galina Daragonova (2013) “Exponential Random Graph Model Fundamentals,” In: (Dean Lusher, Johan Koskinen, and Garry Robins, eds.) Exponential Random Graph Models For Social Networks: Theory, Methods, and Applications, Cambridge University Press. Chapter 6.10.1017/CBO9780511894701.008Search in Google Scholar

Krackhardt, David (1988) “Predicting with Networks: Nonparametric Multiple Regression Analysis of Dyadic Data,” Social networks, 10(4):359–381.10.1016/0378-8733(88)90004-4Search in Google Scholar

Lazer, David, Brian Rubineau, Carol Chetkovich, Nancy Katz and Michael Neblo (2010) “The Coevolution of Networks and Political Attitudes,” Political Communication, 27:248–274.10.1080/10584609.2010.500187Search in Google Scholar

Leider, Jonathon P., Brian C. Castrucci, Jenine K. Harris and Shelley Hearne (2015) “The Relationship of Policymaking and Networking Characteristics among Leaders of Large Urban Health Departments,” International Journal of Environmental Research and Public Health, 12:9169–9180.10.3390/ijerph120809169Search in Google Scholar

Masket, Seth E. (2015) Do Voters and Insiders Nominate the Same Sort of Candidates? A Look at Legislative Vacancy Appointments in Illinois and Colorado. Presented at the UCLA Department of Political Science.Search in Google Scholar

Masket, Seth and Boris Shor (2015) “Polarization without Parties: Term Limits and Legislative Partisanship in Nebraska’s Unicameral Legislature,” State Politics & Policy Quarterly, 15(1):67–90.10.1177/1532440014564984Search in Google Scholar

McClurg, Scott D. and Joseph K. Young (2011) “Political Networks,” PS: Political Science & Politics, 44(01):39–43.Search in Google Scholar

Mooney, Christopher Z. (2001) “Modeling Regional Effects on State Policy Diffusion,” Political Research Quarterly, 54(1):103–124.10.1177/106591290105400106Search in Google Scholar

Newman, Mark E. J. and Juyong Park (2003) “Why Social Networks are Different from other Types of Networks,” Physical Review E, 68(3):036122.10.1103/PhysRevE.68.036122Search in Google Scholar

Oatley, Thomas, William Winecoff, Andrew Pennock and Sarah Bauerle Danzman (2013) “The Political Economy of Global Finance: A Network Model.” Perspectives on Politics, 11(01):133–153.10.1017/S1537592712003593Search in Google Scholar

Ohtsuki, Hisashi, Christoph Hauert, Erez Lieberman and Martin A. Nowak (2006) “A Simple Rule for the Evolution of Cooperation on Graphs and Social Networks,” Nature, 441(7092):502–505.10.1038/nature04605Search in Google Scholar

Poast, Paul (2010) “(Mis) Using Dyadic Data to Analyze Multilateral Events,” Political Analysis, 18(4):403–425.10.1093/pan/mpq024Search in Google Scholar

R Development Core Team (2013) R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Version 3.01. http://www.r-project.org.Search in Google Scholar

Ringe, Nils, Jennifer Nicoll Victor and Christopher J. Carman (2013) Bridging the Information Gap: Legislative member organizations as social networks in the United States and the European Union. University of Michigan Press.10.3998/mpub.4058730Search in Google Scholar

Robins, Garry and Dean Lusher (2013) “Simplified Account of an Exponential Random Graph Model as a Statistical Model,” In: (Dean Lusher, Johan Koskinen and Garry Robins, eds.) Exponential Random Graph Models For Social Networks: Theory, Methods, and Applications, Cambridge University Press. Chapter 4.10.1017/CBO9780511894701.005Search in Google Scholar

Robins, Garry, Pip Pattison, Yuval Kalish and Dean Lusher (2007) “An Introduction to Exponential Random Graph (p*) Models for Social Networks,” Social Networks, 29(2):173–191.10.1016/j.socnet.2006.08.002Search in Google Scholar

Song, Hyunjin (2015) “Uncovering the Structural Underpinnings of Political Discussion Networks: Evidence from an Exponential Random Graph Model,” Journal of Communication, 65:146–169.10.1111/jcom.12140Search in Google Scholar

Stefanski, L. A. (2000) “Measurement Error Models,” Journal of the American Statistical Association, 95(452):1353–358.10.1080/01621459.2000.10474347Search in Google Scholar

Wooldridge, Jeffrey M. (2009) Introductory Econometrics: A Modern Approach, 4e. Stamford(CT): South-Western Cengage Learning.Search in Google Scholar


Supplemental Material

The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/spp-2016-0001).



Article note:

Complete replication data and the appendix will be made available online at the author’s website immediately upon acceptance for publication.


Published Online: 2017-5-11
Published in Print: 2016-12-20

©2016 Walter de Gruyter GmbH, Berlin/Boston

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