Seriation and Multidimensional Scaling: A Data Analysis Approach to Scaling Asymmetric Proximity Matrices

Applied Psychological Measurement

Volumn 16, Issue 2, 1992, Pages 105-117

  Rodgers, Joseph Lee ^a   Thompson, Tony D ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

asymmetric data; cluster analysis; combinatorial data analysis; multidimensional scaling; order analysis; proximity data; seriation; unidimensional scaling

Indexed keywords

EID: 84976943871     PISSN: 01466216     EISSN: 15523497     Source Type: Journal    
DOI: 10.1177/014662169201600201     Document Type: Article

References (41)

1. Baker, F.B., & Hubert, L.J. (1977). Applications of combinatorial programming to data analysis: Seriation using asymmetric proximity measures. British Journal of Mathematical and Statistical Psychology, 30, 154-164.
2. Bentler, P.M. (1986). Structural modeling and Psychometrika: An historical perspective on growth and achievements. Psychometrika, 51, 35-52.
3. Cliff, N., Collins, L., Zatkin, J., Gallipeau, D., & McCormick, D. (1988). An ordinal scaling method for questionnaire and other ordinal data. Applied Psychological Measurement, 12, 83-97.
4. Constantine, A.G., & Gower, J.C. (1978). Graphical representation of asymmetric matrices. Applied Statistics, 27, 297-304.
5. Coombs, C., & Smith, J.E.K. (1973). On the detection of structure in attitudes and developmental processes. Psychological Review, 80, 337-351.
6. Cunningham, J.P. (1978). Free trees and bidirectional trees as representations of psychological distance. Journal of Mathematical Psychology, 17, 165-188.
7. Defays, D. (1978). A short note on a method of seriation. The British Journal of Mathematical and Statistical Psychology, 31, 49-53.
8. DeSarbo, W.S. (1982). GENCLUS: New models for general non-hierarchical clustering analysis. Psychometrika, 47, 449-475.
9. DeSarbo, W.S., Manrai, A., & Burke, R. (1990). A nonspatial methodology for the analysis of two-way proximity data incorporating the distance-density hypothesis. Psychometrika, 55, 229-254.
10. De Soete, G., Hubert, L., & Arabie, P. (1988). On the use of simulated annealing for combinatorial data analysis. In W. Gaul & M. Schader (Eds.), Data, expert knowledge, and decisions (pp. 328-340). Berlin: Springer-Verlag.
11. Flink, S. (1990, February). On top of the world. World Tennis, 31-34.
12. Flueck, J.A., & Korsh, J.R. (1974). A branch search algorithm for maximum likelihood paired comparison ranking. Biometrika, 61, 621-626.
13. Gower, J.C. (1977). The analysis of asymmetry and orthogonality. In J. R. Barra, F. Brodeau, G. Romer, & B. van Cutsem (Eds.), Recent developments in statistics (pp. 109-123). New York/Amsterdam: North Holland.
14. Heiser, W.J. (1981). Unfolding analysis of proximity data. Unpublished doctoral dissertation, University of Leiden, The Netherlands.
15. Holman, E.W. (1979). Monotonic models for asymmetric proximities. Journal of Mathematical Psychology, 20, 1-15.
16. Hubert, L.J. (1974). Some applications of graph theory and related non-metric techniques to problems of approximate seriation: The case for symmetric proximity measures. The British Journal of Mathematical and Statistical Psychology, 27, 133-153.
17. Hubert, L.J. (1976). Seriation using asymmetric proximity measures. The British Journal of Mathematical and Statistical Psychology, 29, 32-52.
18. Hubert, L.J., & Arabie, P. (1987). Unidimensional scaling and combinatorial optimization. In J. De Leeuw, W. J. Heiser, J. Meulman, & F. Critchley (Eds.), Multidimensional data analysis (pp. 181-196). Leiden, The Netherlands: DSWO Press.
19. Hubert, L.J., & Baker, F.B. (1979). Evaluating the symmetry of a proximity matrix. Quality and Quantity, 13, 77-84.
20. Hubert, L.J., & Golledge, R.G. (1981). Matrix reorganization and dynamic programming: Applications to paired comparisons and unidimensional seriation. Psychometrika, 46, 429-442.
21. Hutchinson, J.W. (1989). NETSCAL: A network scaling algorithm for nonsymmetric proximity data. Psychometrika, 54, 25-52.
22. Kendall, M.G. (1955). Further contributions to the theory of paired comparisons. Biometrics, 11, 43-62.
23. Klauer, K.C. (1989). Ordinal network representation: Representing proximities by graphs. Psychometrika, 54, 737-750.
24. Krumhansl, C.L. (1978). Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85, 445-463.
25. Kruskal, J.B., & Wish, M. (1978). Multidimensional scaling. Beverly Hills: Sage.
26. Levin, J., & Brown, M. (1979). Scaling a conditional proximity matrix to symmetry. Psychometrika, 44, 239-244.
27. Lewis, C. (1986). Test theory and Psychometrika: The past twenty-five years. Psychometrika, 51, 11-22.
28. Mardia, K.V., Kent, J.T., & Bibby, J.M. (1979). Multivariate analysis. New York: Academic Press. Mulaik, S.A. (1986). Factor analysis and Psychometrika: Major developments. Psychometrika, 51, 23-34.
29. Rodgers, J.L. (1988). Structural models of the American Psychological Association in 1986: A taxonomy for reorganization. American Psychologist, 43, 372-382.
30. Rodgers, J.L., Thompson, T.D., & Thompson, P.A. (1989). TRIAGE: A preprocessor for proximity data. Psychometrika, 54, 352-353.
31. Saito, T. (1986). Multidimensional scaling to explore complex aspects in dissimilarity judgment. Behaviormetrika, 20, 35-62.
32. SAS Institute, Inc. (1983). SUGI supplemental library user's guide [Computer program manual]. Cary NC: Author.
33. SAS Institute, Inc. (1985). SAS user's guide: Basics [Computer program manual]. Cary NC: Author.
34. Thissen, D., & Steinberg, L. (1988). Data analysis using item response theory. Psychological Bulletin, 104, 385-395.
35. Torgerson, W.S. (1986). Scaling and Psychometrika: Spatial and alternative representations of similarity data. Psychometrika, 51, 57-64.
36. Tukey, J.W. (1977). Exploratory data analysis. Reading MA: Addison-Wesley.
37. Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327-352.
38. Tversky, A., & Hutchinson, J. (1986). Nearest neighbor analysis of psychological spaces. Psychological Review, 93, 3-22.
39. Weeks, D.G., & Bentler, P.M. (1982). Restricted multidimensional scaling models for asymmetric proximities. Psychometrika, 47, 201-208.
40. Young, F.W. (1975, August). An asymmetric Euclidean model for multiprocess asymmetric data. Paper presented at the US-Japan Seminar on Multidimensional Scaling, University of California at San Diego, La Jolla.
41. Younger, D.H. (1963). Minimum feedback arc sets for a directed graph. Institute of Electrical and Electronics Engineers Transactions on Circuit Theory, 10, 238-245.