Curved exponential family models for social networks

Curved exponential family models are a useful generalization of exponential random graph models (ERGMs). In particular, models involving the alternating k-star, alternating k-triangle, and alternating k-twopath statistics of Snijders et al. [Snijders, T.A.B., Pattison, P.E., Robins, G.L., Handcock,...

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Bibliographic Details
Published in:Social networks 2007-05, Vol.29 (2), p.216-230
Main Author: Hunter, David R.
Format: Article
Language:English
Subjects:
Estimation
Exponential random graph model
Mathematical Models
Maximum likelihood estimation
Network Analysis
p-Star model
Probability
Randomness
Social Networks
Statistical models
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Summary:Curved exponential family models are a useful generalization of exponential random graph models (ERGMs). In particular, models involving the alternating k-star, alternating k-triangle, and alternating k-twopath statistics of Snijders et al. [Snijders, T.A.B., Pattison, P.E., Robins, G.L., Handcock, M.S., in press. New specifications for exponential random graph models. Sociological Methodology] may be viewed as curved exponential family models. This article unifies recent material in the literature regarding curved exponential family models for networks in general and models involving these alternating statistics in particular. It also discusses the intuition behind rewriting the three alternating statistics in terms of the degree distribution and the recently introduced shared partner distributions. This intuition suggests a redefinition of the alternating k-star statistic. Finally, this article demonstrates the use of the statnet package in R for fitting models of this sort, comparing new results on an oft-studied network dataset with results found in the literature.
ISSN:0378-8733
1879-2111
DOI:10.1016/j.socnet.2006.08.005