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Dear SOCNETters,

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!).

Thank you!

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.

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