Asymmetric multidimensional scaling of two-mode three-way proximities

Journal of Classification

Volumn 14, Issue 2, 1997, Pages 195-224

  Okada, Akinori ^a   Imaizumi, Tadashi ^b  

^a RIKKYO UNIVERSITY   (Japan)

^b TAMA UNIVERSITY   (Japan)

Author keywords

Asymmetric proximity; Multidimensional scaling; Two mode three way data

Indexed keywords

EID: 0031517183     PISSN: 01764268     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003579900010     Document Type: Article

References (42)

1. ARABIE, P., CARROLL, J. D., and DESARBO, W. S. (1987), Three-Way Scaling and Clustering, Newbury Park, CA: Sage. Translated into Japanese by A. Okada and T. Imaizumi (1990), Tokyo: Kyoroitsu Shuppan.
2. BLOXOM. B. (1968), "Individual Differences in Multidimensional Scaling," Research Bulletin 68-45, Princeton, NJ: Educational Testing Service.
3. CARROLL, J. D. (1972), "Individual Differences and Multidimensional Scaling," in Multidimensional Scaling: Theory and Applications in the Behavioral Sciences: Vol. 1. Theory, Eds., R. N. Shepard, A. K. Romney, and S. B. Nerlove, New York: Seminar Press, 105-155.
4. CARROLL, J. D., and CHANG, J. J. (1970), "Analysis of Individual Differences in Multidimensional Scaling via an N-way Generalization of 'Eckart-Young' Decomposition," Psychometrika, 35, 283-319.
5. CHINO, N. (1978), "A Graphical Technique for Representing the Asymmetric Relationships between N objects," Behaviometrika, 5, 23-40.
6. CHINO, N., and SHIRAIWA, K. (1993), "A Geometrical Structures of Some Non-distance Models for Asymmetric MDS," Behaviometrika, 20, 35-47.
7. CONSTANTINE, A. G., and GOWER, J. C. (1978), "Graphical Representations of Asymmetric Matrices," Applied Statistics, 27, 297-304.
8. CUNNINGHAM, J. P. (1978), "Free Trees and Bidirectional Trees as Representations of Psychological Distances," Journal of Mathematical Psychology, 17, 165-188.
9. DESARBO, W. S., JOHNSON, M. D., MANRAI, A. K., MANRAI, L. A., and EDWARDS, E. A. (1992), "TSCALE: A New Multidimensional Scaling Procedure based on Tversky's Contrast Model," Psychmetrika, 57, 43-69.
10. DESARBO, W. S., and MANRAI, A. K. (1992), "A New Multidimensional Scaling Methodology for the Analysis of Asymmetric Proximity Data in Marketing Research," Marketing Science, 11, 1-20.
11. GOWER, J. C. (1977), "The Analysis of Asymmetry and Orthogonality," in Recent Development in Statistics, Eds., J. R. Barra, F. Brodeau, G. Romier, and B. van Cutsen, Amsterdam: North Holland.
12. GUTTMAN, L. (1968), "A General Nonmetric Technique for Finding the Smallest Coordinate Space for a Configuration of Points," Psychometrika, 33, 469-506.
13. HARSHMAN, R. A. (1978), "Models for Analysis of Asymmetrical Relationships among N objects or Stimuli," Paper presented at the First Joint Meeting of the Psychometric Society and the Society for Mathematical Psychology, MacMaster University, Hamilton, Ontario, Canada.
14. HARSHMAN, R. A., GREEN, P. E., WIND, Y., and LUNDY, M. E. (1982), "A Model for the Analysis of Asymmetric Data in Marketing Research," Marketing Science, 1, 205-242.
15. HORAN, C. B. (1969), "Multidimensional Scaling: Combining Observations When Individuals Have Different Perceptual Structures," Psychometrika, 34, 139-165.
16. KRUSKAL, J. B. (1964a), "Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis," Psychometrika, 29, 1-27.
17. KRUSKAL, J. B. (1964b), "Nonmetric Multidimensional Scaling: A Numerical Method," Psychometrika, 29, 115-129.
18. KRUSKAL, J. B., and CARROLL, J. D. (1969), "Geometric models and badness-of-fit measures," in Multivariate analysis II, Ed., P. K. Krishnaiah, New York: Academic Press, 639-671.
19. LINGOES, J. C., and BORG, I. (1978), "A Quasi-Statistical Model for Choosing between Alternative Configurations Derived from Ordinally Constrained Data," British Journal of Mathematical and Statistical Psychology, 36, 36-53.
20. OKADA, A. (1988a), "Asymmetric Multidimensional Scaling of Car Switching Data," in Data. Expert Knowledge and Decisions, Eds., W. Gaul and M. Schader, Heidelberg: Springer-Verlag, 279-290.
21. OKADA, A. (1988b). "An Analysis of Intergenerational Mobility by Asymmetric Multidimensional Scaling," in The Many Faces of Multivariate Analysis, Eds., M. G. H. Jansen and W. H. van Schuur, Groningen: RION, 1-15.
22. OKADA, A. (1990), "A Generalization of Asymmetric Multidimensional Scaling," in Knowledge, Data and Computer-Assisted Decisions, Heidelberg: Springer-Verlag, 127-138.
23. OKADA, A., and IMAIZUMI, T. (1980), "Nonmetric Method for Extended INDSCAL Model," Behaviometrika, 7, 13-22.
24. OKADA, A., and IMAIZUMI, T. (1987), "Nonmetric Multidimensional Scaling of Asymmetric Proximities," Behaviometrika, 21, 81-96.
25. OKADA, A., and IMAIZUMI, T. (1992), "Multidimensional Scaling Models of Two-Mode Three-Way Asymmetric Proximity Data," Research Report, Rikkyo (St. Paul's) University, 81-96.
26. SAITO, T. (1991), "Analysis of Asymmetric Proximity Matrix by a Model of Distance and Additive Terms," Behaviometrika, 29, 45-60.
27. SCHÖNEMANN, P. H. (1972), "An Algebraic Solution for a Class of Subjective Metrics Models," Psychometrika, 37, 441-451.
28. SEIYAMA, K., NAOI, A., SATO, Y. TSUZUKI, K., and KOJIMA, H. (1990), "Stratification Structure of Contemporary Japan and its Trend," in Social Stratification in Contemporary Japan, Vol. 1. Structure and Process of Social Stratification, Eds., A. Naoi and K. Seiyama, Tokyo: Tokyo University Press, 15-50.
29. SLATER, P. B. (1976), "Hierarchical Internal Migration Regions of France," IEEE Transactions on Systems, Man, and Cybernetics, 6, 321-324.
30. TAKANE, Y., YOUNG, F. W., and DE LEEUW, J. (1977), "Nonmetric Individual Differences Multidimensional Scaling: An Alternating Least Squares Method with Optimal Scaling Features," Psychometrika, 42, 7-67.
31. TOBLER, W. (1977), "Spatial Interaction Patterns," Journal of Environmental Systems, 6, 271-301.
32. TOBLER, W. R. (1979), "Estimation of Attractiveness from Interactions," Environment and Planning A. 11, 121-127.
33. TORGERSON, W. S. (1952), "Multidimensional Scaling: I. Theory and Method," Psychometrika, 17, 401-419.
34. TUCKER, L. R. and MESSICK, S. J. (1963), "An Individual Differences Model for Multidimensional Scaling," Psychometrika, 38, 333-368.
35. TVERSKY, A. (1977), "Features of Similarity," Psychological Review. 84, 327-352.
36. WEEKS, D. G., and BENTLER, P. M. (1982), "Restricted Multidimensional Scaling Models for Asymmetric Proximities," Psychometrika, 47, 201-208.
37. YOUNG, F. W. (1975), "An Asymmetric Euclidean Model for Multi-Process Asymmetric Data," Proceedings of the US-Japan Seminar on the Theory, Methods and Applications of Multidimensional Scaling and Related Techniques, University of California San Diego, La Jolla, CA, 79-88.
38. YOUNG, F. W. (1987), Multidimensional Scaling: History, Theory and Applications, Hillsdale, NJ: Erlbaum.
39. ZIELMAN, B. (1991), "Three-Way Scaling of Asymmetric Proximities," Research Report RR91-01. Department of Data Theory, University of Leiden.
40. ZIELMAN, B., and HEISER, W. J. (1991), "Analysis of Asymmetry by a Slide-Vector," Research Report RR91-05, Department of Data Theory, University of Leiden.
41. ZIELMAN, B., and HEISER, W. J. (1993), "Analysis of Asymmetry by a Slide-Vector," Psychometrika, 58, 101-114.
42. ZIELMAN, B., and HEISER, W. J. (1996), "Models for Asymmetric Proximities," British Journal of Mathematical and Statistical Psychology, 49, 127-146.