Clusterwise p* models for social network analysis

Statistical Analysis and Data Mining

Volumn 4, Issue 5, 2011, Pages 487-496

  Steinley, Douglas ^a   Brusco, Michael J ^b   Wasserman, Stanley ^c  

^a UNIVERSITY OF MISSOURI   (United States)

^b FLORIDA STATE UNIVERSITY   (United States)

^c INDIANA UNIVERSITY   (United States)

Author keywords

Blockmodeling; Cluster analysis; Social network analysis

Indexed keywords

GRAPH THEORY;

BLOCKMODELING; DEGENERACY PROBLEMS; EXPONENTIAL RANDOM GRAPH MODEL; GRAPH STRUCTURES; LOCAL ESTIMATION; NETWORK MODELS; P-MODEL; SOCIAL INTERACTIONS; SOCIAL NETWORK ANALYSIS;

CLUSTER ANALYSIS;

EID: 80053070101     PISSN: 19321872     EISSN: 19321864     Source Type: Journal    
DOI: 10.1002/sam.10139     Document Type: Article

References (45)

1. S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications, New York, Cambridge, 1994.
2. F. Lorrain and H. C. White, Structural equivalence of individuals in social networks, J Math Sociol 1 (1971), 49-80.
3. L. Hubert, Data analysis implications of some concepts related to the cuts of a graph, J Math Psychol 15 (1977), 199-208.
4. P. Doreian, V. Batagelj, and A. Ferligoj, Generalized Blockmodeling, Cambridge University Press, Cambridge, 2005.
5. M. J. Brusco and D. Steinley, Inducing a blockmodel structure on two-mode data using seriation procedures, J Math Psychol 50 (2006), 468-477.
6. P. E. Pattison and R. L. Breiger, Lattices and dimensional representations: Matrix decompositions and ordering structures, Social Netw 24 (2002), 423-444.
7. M. J. Brusco and D. Steinley, An evaluation of a variable-neighborhood search method for blockmodeling of two-mode binary matrices based on structural equivalence, J Math Psychol 51 (2007), 325-338.
8. M. J. Brusco and D. Steinley, Integer programs for one- and two-mode blockmodeling based on prespecified image matrices for structural and regular equivalence, J Math Psychol 53 (2009), 577-585.
9. M. J. Brusco and D. Steinley, A tabu search heuristic for deterministic two-mode blockmodeling of binary network matrices, Psychometrika, in press.
10. D. Steinley, K-means clustering: a half-century synthesis, Brit J Math Stat Psychol 59 (2006), 1-34.
11. H.-F. Köhn, D. Steinley, and M. J. Brusco, The p-median model as a tool for clustering psychological data, Psychol Meth 15 (2010), 87-95.
12. S. Wasserman and C. A. Anderson, Stochastic a posteriori blockmodels: construction and assessment, Social Netw 9 (1987), 1-36.
13. K. Nowicki and T. A. B. Snijders, Estimation and prediction for stochastic blockstructures, J Am Stat Assoc 96 (2001), 1077-1087.
14. E. M. Airoldi, D. Blei, S. Fienberg, and E. P. Xing, Mixed membership stochastic blockmodels, J Mach Learn Res 9 (2008), 1981-2014.
15. M. S. Handcock, A. E. Raftery, and J. Tantrum, Model-based clustering for social networks (with discussion), J R Stat Soc A 170 (2007), 301-354.
16. P. D. Hoff, A. E. Raftery, and M. S. Handcock, Latent space approaches to social network analysis, J Am Stat Assoc 97 (2002), 1090-1098.
17. J. E. Besag, Spatial interaction and the statistical analysis of lattice systems (with discussion), J R Stat Assoc B 36 (1974), 192-236.
18. S. Wasserman and P. Pattison, Statistical models for social networks, In Studies in Classification, Data Analysis, and Knowledge Organization, H. Kiers, J. Rasson, P. Groenen, and M. Schader, eds. Heidelberg, Springer, 2000.
19. *, Psychometrika 60 (1996), 401-426.
20. P. Pattsion and S. Wasserman, Logit models and logistic regressions for social networks: II. Multivariate relations, Brit J Math Stat Psychol 52 (1999), 169-193.
21. G. L. Robins, P. Pattison, and S. Wasserman, Logit models and logistic regressions for social networks: III. Valued relations, Psychometrika 64 (1999), 371-394.
22. G. L. Robins, P. Pattison, and P. Elliott, Network models for social influence processes, Psychometrika 66 (2001), 161-190.
23. P. Pattison and G. L. Robins, Neighbourhood-based models for social networks, Sociol Methodol 32 (2002), 301-337.
24. *: Monte Carlo maximum likelihood estimation, In Paper presented at International Conference on Social Networks, Sitges, Spain, May 1999, 28-31.
25. M. S. Handcock, Statistical models for social networks: inference and degeneracy, In Dynamic Social Network Modeling and Analysis, R. Breiger, K. Carley, and P. Pattison, eds. Washington, DC, National Academies Press, 2003, 220-240.
26. T. A. B. Snijders, Markov chain Monte Carlo estimation of exponential random graph models, J Social Struct 3 (2002), 2.
27. J. E. Besag, Statistical analysis of non-lattice data, The Statistician 24 (1975), 179-195.
28. J. E. Besag, Efficiency of pseudo-likelihood estimation for simple Gaussian random fields, Biometrika 64 (1977), 616-618.
29. D. Strauss, On a general class of models for interaction, SIAM Rev 28 (1986), 513-527.
30. D. Strauss and M. Ikeda, Pseduolikelihood estimation for social networks, J Am Stat Assoc 85 (1990), 204-212.
31. *) models for social networks, Social Netw 29 (2007), 192-215.
32. H. Späth, Algorithm 39: clusterwise linear regression, Computing 22 (1979), 367-373.
33. H. Späth, Algorithm 48: a fast algorithm for clusterwise linear regression, Computing 29 (1982), 175-181.
34. H. Späth, Mathematical Algorithms for Linear Regression, San Diego, CA, Academic, 1991.
35. M. J. Brusco, J. D. Cradit, D. Steinley, and G. Fox, Cautionary remarks on the use of clusterwise regression, Multivariate Behav Res 43 (2008), 29-49.
36. D. Steinley, Local optima in K-means clustering: What you don't know may hurt you, Psychol Methods 8 (2003), 294-304.
37. D. Steinley and M. J. Brusco, A new variable weighting and selection procedure for K-means cluster analysis, Multivariate Behav Res 43 (2008), 77-108.
38. D. W. Hosmer and S. Lemeshow, Applied Logistic Regression, (2nd ed.), New York, Wiley, 2004.
39. M. J. Brusco, Clustering binary data in the presence of masking variables, Psych Meth 9 (2004), 510-523.
40. D. Steinley and M. J. Brusco, Initializing K-means batch clustering: a critical evaluation of several techniques, J Classif 24 (2007), 99-121.
41. D. Steinley and M. J. Brusco, Evaluating the performance of model-based clustering: recommendations and cautions, Psychol Meth 16 (2011), 63-79.
42. F. S. Sampson, A novitiate in a period of change: An experimental and case study of social relationships, Unpublished Doctoral Dissertation, Cornell University, 1968.
43. R. Breiger, S. Boorman, and P. Arabie, An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling, J Math Psychol 12 (1975), 328-383.
44. D. Steinley, Properties of the Hubert--Arabie adjusted Rand index, Psychol Meth 9 (2004), 386-396.
45. V. Batagelj and A. Mrvar, Pajek datasets. 2006. [Last Accessed June 2011].