Inference in curved exponential family models for networks

Journal of Computational and Graphical Statistics

Volumn 15, Issue 3, 2006, Pages 565-583

  Hunter, David R ^a   Handcock, Mark S ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Exponential random graph model; Markov chain Monte Carlo; Maximum likelihood estimation; p star model

Indexed keywords

EID: 33749665991     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186006X133069     Document Type: Review

References (33)

1. Barndorff-Nielsen, O. E. (1978), Information and Exponential Families in Statistical Theory New York: Wiley.
2. Besag, J. (1974), "Spatial Interaction and the Statistical Analysis Of Lattice Systems," Journal of the Royal Statistical Society, Series B, 36, 192-225.
3. _ (2000), "Markov Chain Monte Carlo for Statistical Inference," Working Paper no. 9, Center for Statistics and the Social Sciences, University of Washington. Available online at http://www.csss.washington.edu/Papers/.
4. Besag, J., and Clifford, P. (1989), "Generalized Monte Carlo Significance Tests," Biometrika, 36, 633-642.
5. Corander, J., Dahmström, K., and Dahmström, P. (1998), "Maximum Likelihood Estimation for Markov Graphs," Research Report 1998:8, Department of Statistics, University of Stockholm.
6. Cowles, M. K., Roberts, G. O., and Rosenthal, J. S. (1999), "Possible Biases Induced by MCMC Convergence Diagnostics," Journal of Statistical Computation and Simulation, 64, 87-104.
7. Crouch, B., Wasserman, S., and Trachtenberg, F. (1998), "Markov Chain Monte Carlo Maximum Likelihood Estimation for p* Social Network Models," paper presented at the XVIII International Sunbelt Social Network Conference in Sitga, Spain.
8. Dahmström, K., and Dahmström, P. (1993), "ML-Estimation of the Clustering Parameter in a Markov Graph Model," Stockholm: Research report, Department of Statistics.
9. Efron, B. (1975), "Defining the Curvature of a Statistical Problem (With Applications to Second Order Efficiency)" (with discussion), The Annals of Statistics, 3, 1189-1242.
10. _ (1978), "The Geometry of Exponential Families," The Annals of Statistics, 6, 362-376.
11. Frank, O. (1991), "Statistical Analysis of Change in Networks," Statistica Neerlandica, 45, 283-293.
12. Frank, O., and Strauss, D. (1986), "Markov Graphs," Journal of the American Statistical Association, 81, 832-842.
13. Gelman, A. (1996), "Inference and Monitoring Convergence," in Practical Markov Chain Monte Carlo, eds. W. R. Gilks, D. J. Spiegelhalter, and S. Richardson, London: Chapman and Hall, pp. 131-144.
14. Gelman, A., and Meng, X.-L. (1998), "Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling," Statistical Science, 13, 163-185.
15. Geyer, C. J. (1994), "On the Convergence of Monte Carlo Maximum Likelihood Calculations," Journal of the Royal Statistical Society, Series B, 56, 261-274.
16. Geyer, C. J., and Thompson, E. (1992), "Constrained Monte Carlo Maximum Likelihood for Dependent Data," Journal of the Royal Statistical Society, Series B, 54, 657-699.
17. Handcock, M. S. (2002), "Statistical Models for Social Networks: Inference and Degeneracy," in Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers, eds. R. Breiger, K. Carley, and P. E. Pattison, National Research Council of the National Academies, Washington, DC: The National Academies Press, pp. 229-240.
18. _ (2003), "Assessing Degeneracy in Statistical Models of Social Networks," Working Paper no. 39, Center for Statistics and the Social Sciences, University of Washington. Available online at http://www.csss. washington.edu/Papers/.
19. Holland, P. W., and Leinhardt, S. (1981), "An Exponential Family of Probability Distributions for Directed Graphs," Journal of the American Statistical Association, 76, 33-50.
20. Hunter, D. R., Goodreau, S. M., and Handcock, M. S. (2005), "Goodness of Fit of Social Network Models," Technical report 05-02, Penn State University Department of Statistics. Available online at http://www.stat.psu.edu/reports/2005.
21. Lazega, E. (2001), The Collegial Phenomenon: The Social Mechanisms of Cooperation Among Peers in a Corporate Law Partnership, Oxford: Oxford University Press.
22. Lazega, E., and Pattison, P. E. (1999), "Multiplexity, Generalized Exchange and Cooperation in Organizations: A Case Study," Social Networks, 21, 67-90.
23. Lehmann, E. L. (1983), Theory of Point Estimation, New York: Wiley.
24. Meng, X.-L., and Wong, W. H. (1996), "Simulating Ratios of Normalizing Constants via a Simple Identity: A Theoretical Exploration," Statistica Sinica, 6, 831-860.
25. Meyn, S. P., and Tweedie, R. L. (1993), Markov Chains and Stochastic Stability, London: Springer-Verlag.
26. Raftery, A.E., and Lewis, S.M. (1996), "Implementing MCMC," in Practical Markov Chain Monte Carlo, eds. W. R. Gilks, D. J. Spiegelhalter, and S. Richardson, London: Chapman and Hall, pp. 115-130.
27. Robbins, H., and Monro, S. (1951), "A Stochastic Approximation Method," Annals of Mathematical Statistics, 22, 400-407.
28. Roberts, G. O. (1996), "Markov Chain Concepts Related to Sampling Algorithms," in Markov Chain Monte Carlo in Practice, eds. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, New York: Chapman and Hall, pp. 45-57
29. Snijders, T. A. B. (2002), "Markov Chain Monte Carlo Estimation of Exponential Random Graph Models," Journal of Social Structure, 3. Available online at www.cmu.edu/joss/content/articles/volume3/Snijders.pdf.
30. Snijders, T. A. B., Pattison, P. E., Robins, G. L., and Handcock, M.S. (2006), "New Specifications for Exponential Random Graph Models," to appear in Sociological Methodology, 36.
31. Strauss, D., and Ikeda, M. (1990), "Pseudolikelihood Estimation for Social Networks," Journal of the American Statistical Association, 85, 204-212.
32. Wasserman, S., and Faust, K. (1994), Social Network Analysis: Methods and Applications, Cambridge, UK: Cambridge University Press.
33. Wasserman, S., and Pattison, P. E. (1996), "Logit Models and Logistic Regression for Social Networks: I. An Introduction to Markov Graphs and p*," Psychometrika, 61, 401-425.