I think I am not alone in not fully appreciating why there is a need for special statistical models for networks (ERGMs, SIENA, etc.). I can accept that there is such a need, but I'd like to understand what dependencies between observations do to traditional models or obvious approaches.
E.g., in a March 16th email, Elly Power had asked about using centrality as a covariate; there were helpful replies from Philip Leifeld, Tom Snijders, and Phillip Bonacich, but aside from there being more suitable alternatives, the effects of dependencies are still opaque to me.
Does anybody know of literature or resources that explain this?
In what I've found so far, the network autocorrelation literature (and 'Galton's problem') from Dow and colleagues in the 80s helps a lot for understanding problems with regression on node attributes, as does Shalizi & Thomas (2011) for C&F's 'network effects' approach. Still, I'd like to see similar explorations for other obvious approaches including using centrality as a covariate, or doing a logistic regression on the presence/absence of individual edges (not pairs of edges as in p1), or perhaps doing a regression with network-level measures of ego networks. What would we be missing? How misleading could results be?
As a related point, does anybody know of introductions that gather up and compare all approaches to network statistics? E.g., I don't think I've seen any introduction that has even just ERGMs and SIENA side-by-side, let alone network autocorrelation with those two, even if just to say what the differences are in modeling goals and assumptions (or, for the former two, to note the range of Tom Snijders' contributions!).
Partial list of what I've been searching through:
- Aral, S., Muchnik, L., and Sundararajan, A. (2009). Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks. Proceedings of the National Academy of Sciences, 106(51):21544–21549. http://www.pnas.org/content/106/51/21544.abstract
- Chatterjee, S., Diaconis, P., and Sly, A. (2011). Random graphs with a given degree sequence. The Annals of Applied Probability, 21(4):1400–1435. http://projecteuclid.org/euclid.aoap/1312818840
- Dekker, D., Krackhardt, D., and Snijders, T. (2007). Sensitivity of MRQAP tests to collinearity and autocorrelation conditions. Psychometrika, 72(4):563–581. http://link.springer.com/article/10.1007%2Fs11336-007-9016-1
- Dow, M. M. (2007). Galton’s problem as multiple network autocorrelation effects: Cultural trait transmission and ecological constraint. Cross-Cultural Research, 41(4):336–363. http://ccr.sagepub.com/content/41/4/336.abstract
- Dow, M. M., Burton, M. L., and White, D. R. (1982). Network autocorrelation: A simulation study of a foundational problem in regression and survey research. Social Networks, 4(2):169–200. http://www.sciencedirect.com/science/article/pii/0378873382900314
- Dow, M. M., Burton, M. L., White, D. R., and Reitz, K. P. (1984). Galton’s problem as network autocorrelation. American Ethnologist, 11(4):754–770. http://onlinelibrary.wiley.com/doi/10.1525/ae.1984.11.4.02a00080/abstract
- Dow, M. M., White, D. R., and Burton, M. L. (1982). Multivariate modeling with interdependent network data. Cross-Cultural Research, 17(3-4):216–245. http://ccr.sagepub.com/content/17/3-4/216.abstract
- Fienberg, S. E. (2012). A brief history of statistical models for network analysis and open challenges. Journal of Computational and Graphical Statistics, 21(4):825–839. http://www.tandfonline.com/doi/abs/10.1080/10618600.2012.738106
- Goldenberg, A., Zheng, A. X., Fienberg, S. E., and Airoldi, E. M. (2010). A survey of statistical network models. Foundations and Trends in Machine Learning, 2(2):129–233. http://arxiv.org/abs/0912.5410
- Hanneman, R. A. and Riddle, M. (2005). Chapter 18: Some statistical tools. In Introduction to social network methods. University of California, Riverside. http://faculty.ucr.edu/~hanneman/nettext/C18_Statistics.html
- Holland, P. W., & Leinhardt, S. (1981). An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association, 76(373):33-50. http://www.jstor.org/stable/2287037
- Hunter, D. R., Krivitsky, P. N., and Schweinberger, M. (2012). Computational statistical methods for social network models. Journal of Computational and Graphical Statistics, 21(4):856–882. http://www.tandfonline.com/doi/abs/10.1080/10618600.2012.732921
- Knoke, D. and Yang, S. (2008). Chapter 5: Advanced methods for analyzing networks. In Social Network Analysis (pp. 91–117), 2nd ed. Quantitative Applications in the Social Sciences, no. 154. SAGE Publications.
- Kolaczyk, E. D. (2009). Statistical analysis of network data: Methods and models. Springer Series in Statistics. Springer-Verlag. http://www.springer.com/us/book/9780387881454
- Kolaczyk, E. D. and Csárdi, G. (2014). Statistical analysis of network data with R. Use R!, volume 65. Springer-Verlag. http://www.springer.com/us/book/9781493909827
- Krackardt, D. (1987). QAP partialling as a test of spuriousness. Social Networks, 9(2):171–186. http://www.sciencedirect.com/science/article/pii/0378873387900128
- Krackhardt, D. (1988). Predicting with networks: Nonparametric multiple regression analysis of dyadic data. Social Networks, 10(4):359–381. http://www.sciencedirect.com/science/article/pii/0378873388900044
- Laumann, E. O., Marsden, P. V., and Galaskiewicz, J. (1977). Community-elite influence structures: Extension of a network approach. American Journal of Sociology, 83(3):594–631. http://www.jstor.org/stable/2778146
- Leenders, R. T. (2002). Modeling social influence through network autocorrelation: Constructing the weight matrix. Social Networks, 24(1):21–47. http://www.sciencedirect.com/science/article/pii/S0378873301000491
- Lusher, D., Koskinen, J., and Robins, G. (2012). Exponential Random Graph Models for social networks: Theory, methods, and applications. Structural Analysis in the Social Sciences. Cambridge University Press.
- Pattison, P., and Robins, G. (2008). Chapter 18: Probabilistic network analysis. In T. Rudas (Ed.), Handbook of Probability: Theory and Applications (pp. 291–313). SAGE Publications. http://dx.doi.org/10.4135/9781452226620
- Prell, C. (2011). Chapter 10: Statistical models for social networks. In Social Network Analysis: History, theory and methodology (pp. 199–220). SAGE Publications.
- Rinaldo, A., Petrovic, S., and Fienberg, S. E. (2013). Maximum lilkelihood estimation in the β-model. The Annals of Statistics, 41(3):1085–1110. http://projecteuclid.org/euclid.aos/1371150894
- Robins, G. (2012). Exponential random graph (p*) models for social networks. In R. A. Meyers (Ed.), Computational Complexity (pp. 2953–2967). Springer New York.http://link.springer.com/referenceworkentry/10.1007%2F978-1-4614-1800-9_182
- Robins, G. (2013). A tutorial on methods for the modeling and analysis of social network data. Journal of Mathematical Psychology, 57(6):261–274.
- Robins, G. (2014). Exponential random graph models for social networks. In J. Scott and P. J. Carrington (Eds.), The SAGE Handbook of Social Network Analysis (pp. 484–501). SAGE Publications. http://www.sciencedirect.com/science/article/pii/S0022249613000126
- Robins, G., Pattison, P., Kalish, Y., and Lusher, D. (2007). An introduction to exponential random graph (p*) models for social networks. Social Networks, 29(2):173–191. Special Section: Advances in Exponential Random Graph (p*) Models. http://www.sciencedirect.com/science/article/pii/S0378873306000372
- Shalizi, C. R. and Thomas, A. C. (2011). Homophily and contagion are generically confounded in observational social network studies. Sociological Methods & Research, 40(2):211–239. http://smr.sagepub.com/content/40/2/211.abstract
- Snijders, T. A. (2011). Statistical models for social networks. Annual Review of Sociology, 37(1):131–153. http://www.annualreviews.org/doi/abs/10.1146/annurev.soc.012809.102709
- Snijders, T. A. and Borgatti, S. P. (1999). Non-parametric standard errors and tests for network statistics. Connections, 22(2):61–70. http://www.insna.org/PDF/Connections/v22/1999_I-2_61-70.pdf
- Snijders, T. A., van de Bunt, G. G., and Steglich, C. E. (2010). Introduction to stochastic actor-based models for network dynamics. Social Networks, 32(1):44–60. http://www.sciencedirect.com/science/article/pii/S0378873309000069
- Snijders, T. A. B. (2014). Network dynamics. In J. Scott and P. J. Carrington (Eds.), The SAGE Handbook of Social Network Analysis (pp. 501–513). SAGE Publications.
- Snijders, T. A. B., Koskinen, J., and Schweinberger, M. (2010b). Maximum likelihood estimation for social network dynamics. The Annals of Applied Statistics, 4(2):567–588. http://projecteuclid.org/euclid.aoas/1280842131
- Steglich, C., Snijders, T. A. B., and Pearson, M. (2010). Dynamic networks and behavior: Separating selection from influence. Sociological Methodology, 40(1):329–393. http://smx.sagepub.com/content/40/1/329
- van Duijn, M. A. J. and Huisman, M. (2014). Statistical models for ties and actors. In J. Scott and P. J. Carrington (Eds.), The SAGE Handbook of Social Network Analysis (pp. 459–483). SAGE Publications.