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13 - Models for Networks

from Part III - Making Structural Predictions

Published online by Cambridge University Press:  21 September 2023

Craig M. Rawlings
Duke University, North Carolina
Jeffrey A. Smith
Nova Scotia Health Authority
James Moody
Duke University, North Carolina
Daniel A. McFarland
Stanford University, California
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Where do networks come from? Numerous theories direct us to the causes of networks (e.g., homophily, triadic closure, physical proximity), some emphasizing outside factors (exogenous causes) and others emphasizing point-in-time network structure (endogenous causes) as shaping a network’s future trajectory. So far, we have examined such causal theories using cross-sectional snapshots in the form of metrics (centrality, density), partitions (clusters), and maps or spaces (visualization). These approaches generally suffer from a lack of stochastic features and observational overdetermination: for example, we observe a pattern in a given school on a given day, but that pattern could result from actor preferences and constraints in the setting. Disentangling such effects requires an inferential approach to probabilistically examine various effects. To the extent that we want to identify causal forces shaping the networks, understanding the unfolding of relations in time – how the individual ties in a network (the dyads joined by one or more relations) and the entire structure of these relations emerge and evolve – is crucial for testing network theories.

Network Analysis
Integrating Social Network Theory, Method, and Application with R
, pp. 301 - 339
Publisher: Cambridge University Press
Print publication year: 2023

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Suggested Further Reading

Anderson, Carolyn J., Wasserman, Stanley, and Crouch, Bradley. 1999. “A p* Primer: Logit Models for Social Networks.” Social Networks 21: 3766. (An early paper on the ERGM/p* approach that still provides a good intuitive understanding of how effects are coded and modeled.)Google Scholar
Butts, Carter T. 2008. “A Relational Events Framework for Social Action.” Sociological Methodology 38: 155200. (Introduces a family of models for dynamic event data and sparked much recent work on modeling dynamic networks generally.)Google Scholar
Cranmer, Skyler J., Desmarais, Bruce A, and Morgan, Jason W. 2020. Inferential Network Analysis. Cambridge: Cambridge University Press. (An excellent overview of ERGM and latent-space models, with detailed examinations of model fit and degeneracy issues and multiple data-type extensions.)Google Scholar
Duxbury, Scott. 2022. Longitudinal Network Models. Thousand Oaks, CA: Sage. (Provides excellent background and instruction on the most common statistical models for longitudinal network data.)Google Scholar
Frank, Ove, and Strauss, David. 1986. “Markov Graphs.” Journal of the American Statistical Association 81: 832–42. (A classic reference that provides the statistical foundations for graph dependencies necessary for parameter estimation on network properties.)Google Scholar
Holland, Paul W., and Leinhardt, Samuel. 1981. “An Exponential Family of Probability Distributions for Directed Graphs.” Journal of the American Statistical Association 76: 3350. (Classic work that sets the stage for the growth of network statistical models in the 1990s.)CrossRefGoogle Scholar
Kolaczyk, Eric D. 2009. Statistical Analysis of Network Data. New York: Springer Press. (A comprehensive and rigorous overview of network models.)Google Scholar
Kuskova, Valentina, and Wasserman, Stanley. 2020. “An Introduction to Statistical Models for Networks.” Pp. 219–33 in The Oxford Handbook of Social Networks, edited by Ryan, Light and Moody, James. New York: Oxford University Press. (Provides an excellent history and general overview of statistical modeling for networks.)Google Scholar
Lusher, Dean, Koskinen, Johan, and Robins, Gary (eds.). 2012. Exponential Random Graph Models for Social Networks: Theory, Methods and Applications. New York: Cambridge University Press. (This edited volume includes clear explanations and mathematical foundations for ERGMs and extensions. Includes numerous applications that provide guidance on the practical use and interpretation of complicated models. See also Lusher et al. 2020.)Google Scholar
Lusher, Dean, Wang, Peng, Brennecke, Julia et al. 2020. “Advances in Exponential Random Graph Models.” Pp. 234–53 in The Oxford Handbook of Social Networks, edited by Light, Ryan and Moody, James. New York: Oxford University Press.Google Scholar
Statnet Development Team (Krivitsky, Pavel N, Handcock, Mark S, Hunter, David R et al.). 2003–20. statnet: Software tools for the Statistical Modeling of Network Data. (This group of researchers has been pushing the development of statistical models for networks for nearly twenty years. The website includes multiple tutorials and further references.)Google Scholar
Wasserman, Stanley. 1977. “Random Directed Graph Distributions and the Triad Census in Social Networks.” Journal of Mathematical Sociology 5: 6186. (An early paper on random graph distributions, essential for testing triadic distributions against underlying volume features.)CrossRefGoogle Scholar

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