Estimation and prediction for stochastic blockmodels for graphs with latent block structure

Journal of Classification

Volumn 14, Issue 1, 1997, Pages 75-100

  Snijders, Tom A B ^a   Nowicki, Krzysztof ^b  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b LUND UNIVERSITY   (Sweden)

Author keywords

Colored graph; EM algorithm; Gibbs sampling; Latent class model; Social network

Indexed keywords

EID: 0031495186     PISSN: 01764268     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003579900004     Document Type: Article

References (40)

1. ANDERSON, C. J., WASSERMAN, S., and FAUST, K. (1992), "Building Stochastic Blockmodels," Social Networks, 14, 137-161.
2. ARABIE P., DOORMAN, S. A., and LEVTTT, P.R. (1978), "Constructing Blockmodels: How and Why," Journal of Mathematical Psychology, 17, 21-63.
3. BJØRNSTAD, J. F. (1990), "Predictive Likelihood: A Review" (with discussion), Statistical Science, 1, 242-265.
4. BOLLOBÁS, B. (1985), Random Graphs, New York: Academic Press.
5. BORGATTI, S., EVERETT, M. G., and FREEMAN, L. C. (1992), UCINET IV Version 1.0 Reference Manual, Columbia, SC: Analytic Technologies.
6. BREIGER, R. L., BOORMAN, S. A., and ARABIE, P. (1975), "An Algorithm for Clustering Relational Data, with Applications to Social Network Analysis and Comparison with Multidimensional Scaling," Journal of Mathematical Psychology, 12, 328-383.
7. BURT, R. S. (1976), "Positions in Networks," Social Forces, 55, 93-122.
8. BUTLER, R. (1986), "Predictive Likelihood Inference with Applications" (with discussion), Journal of the Royal Statistical Society, Series B, 481, 1-38.
9. CASELLA, G., and GEORGE, E. I. (1992), "Explaining the Gibbs Sampler," American Statistician, 46, 167-174.
10. DEMPSTER, A. P., LAIRD, N. M., and RUBIN, D. B. (1977), "Maximum Likelihood from Incomplete Data via the EM Algorithm" (with discussion), Journal of the Royal Statistical Society, Series B, 39, 1-38.
11. ERDÖS, P., and RÉNYI, A. (1959), "On Random Graphs 1," Publications in Mathematics, Debrecen, 6, 290-297.
12. ERDÖS, P., and RÉNYI, A. (1960), "On the Evolution of Random Graphs," Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 5, 17-61.
13. FAUST, K. (1988), "Comparison of Methods for Positional Analysis: Structural and General Equivalences," Social Networks, 10, 313-341.
14. FAUST, K., and WASSERMAN, S. (1992), "Blockmodels: Interpretation and Evaluation," Social Networks, 14, 5-61.
15. FELLER, W. (1968), An Introduction to Probability Theory and its Applications, Vol. I, New York: Wiley.
16. FIENBERG, S. E., MEYER, M. M., and WASSERMAN, S. (1985), "Statistical Analysis of Multiple Sociometric Relations," Journal of the American Statistical Association, 80, 51-67.
17. FIENBERG, S. E., and WASSERMAN, S. (1981), "Categorical Data Analysis of Single Sociometric Relations," in Sociological Methodology - 1981, Ed., S. Leinhardt, San Francisco, CA: Jossey-Bass, 156-192.
18. FRANK, O. (1988), "Triad Count Statistics," Discrete Mathematics, 72, 141-149.
19. FRANK, O. (1988), "Random Sampling and Social Networks: A Survey of Various Approaches," Mathématiques, Informatique et Sciences Humaines, 26:104, 19-33.
20. FRANK, O., and HARARY, F. (1982), "Cluster Inference by Using Transitivity Indices in Empirical Graphs," Journal of the American Statistical Association, 81, 835-840.
21. FRANK, O., and NOWICKI, K. (1993), "Exploratory Statistical Analysis of Networks," Annals of Discrete Mathematics, 55, 349-366.
22. GELFAND, A. E., and SMITH, A. F. M. (1990), "Sampling-based Approaches to Calculating Marginal Densities," Journal of the American Statistical Association, 85, 398-409.
23. GELMAN, A., and RUBIN, D. B. (1992), "Inference from Iterative Simulation Using Multiple Sequences" (with discussion), Statistical Science, 7, 457-511.
24. GEMAN, S., and GEMAN, D. (1983), "Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI 6, 721-741.
25. GRUSHO, A. A. (1982), "Certain Statistic Problems on Graphs," Matematicheskie Zametki, 36, 269-277.
26. HANSELL, S. (1984), "Cooperative Groups, Weak Ties, and the Integration of Peer Friendships," Social Psychology Quarterly, 76, 316-328.
27. HOLLAND, P., LASKEY, K. B., and LEINHARDT, S. (1983), "Stochastic Blockmodels: Some First Steps," Social Networks, 5, 109-137.
28. HOLLAND, P., and LEINHARDT, S. (1981). "An Exponential Family of Probability Distributions for Directed Graphs," Journal of the American Statistical Association, 76, 33-50.
29. JANSON, S., and NOWICKI, K. (1991), "The Asymptotic Distributions of Generalized U-Statistics with Applications to Random Graphs," Probability Theory and Related Fields, 90, 341-375.
30. LEHMANN, E. L. (1983), Theory of Point Estimation, New York: Wiley.
31. LORRAIN, F., and WHITE, H. C. (1971). "Structural Equivalence of Individuals in Social Networks," Journal of Mathematical Sociology, 1, 49-80.
32. MATHIASEN, P. E. (1979), "Prediction Functions," Scandinavian Journal of Statistics, 6, 1-21.
33. PRESS, S. J. (1989), Bayesian Statistics, New York: Wiley.
34. SCHWARTZ, J. E. (1977), "An Examination of CONCOR and Related Methods for Blocking Sociometric Data," in Sociological Methodology - 1977, Ed., D. Heise, San Francisco, CA: Jossey-Bass, 255-282.
35. SCOTT, J. (1991), Social Network Analysis: A Handbook, Newbury Park, CA: Sage Publications.
36. WANG, Y. J., and WONG, G. Y. (1987), "Stochastic Blockmodels for Directed Graphs," Journal of the American Statistical Association, 82, 8-19.
37. WASSERMAN, S., and ANDERSON, C. (1987), "Stochastic a posteriori Blockmodels: Construction and Assessment," Social Networks, 9, 1-36.
38. WASSERMAN, S., and FAUST, K. (1994), Social Network Analysis: Methods and Applications, Cambridge and New York: Cambridge University Press.
39. 1: External Constraints, Interactions and Non-binary Relations," Social Networks, 6, 177-192.
40. WELLMAN, B., FRANK, O., ESPINOZA, V., LUNDQUIST, S., and WILSON, C. (1991), "Integrating Individual, Relational and Structural Analysis," Social Networks, 13, 223-249.