Distance models for three-way tables and three-way association

Journal of Classification

Volumn 19, Issue 1, 2002, Pages 161-178

  De Rooij, Mark ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

INDSCAL; Second order odds ratio; Three way two mode data; Triadic distance; Weighted Euclidean distance

Indexed keywords

EID: 0036882185     PISSN: 01764268     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00357-001-0037-7     Document Type: Article

References (29)

1. AGRESTI, A., (1990), Categorical Data analysis, New York: Wiley.
2. ARABIE, P., CARROLL, J.D., and DESARBO, W.S. (1987), Three-Way Scaling and Clustering, Newbury Park, CA: Sage.
3. BERNARD, M. CL., and LAVIT, CH. (1985), "Présentation des Donnees," Statistique et Analyse des Données, 10, 11-15.
4. BISHOP, Y. M. M., FIENBERG, S. E., and HOLLAND, P. W. (1975), Discrete Multivariate Analysis: Theory and Practice, Cambridge, MA: MIT press.
5. 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.
6. CARROLL, J. D., and CHANG, J. J. (1972), "IDIOSCAL (Individual Differences in Orientation SCALing): A Generalization of INDSCAL Allowing IDIOsyncratic Reference Systems as well as an Analytic Approximation to INDSCAL," Paper presented at meeting of the Psychometric Society, Princeton.
7. CARROLL, J. D., and WISH, M. (1974). Models and Methods for Three-Way Multidimensional Scaling, in Contemporary Developments in Mathematical Psychology, Eds., D. H. Krantz, R. C. Atkinson, R. D. Luce, and P. Suppes, San Francisco: Freeman, pp. 57-105.
8. COX, T. F., COX, M. A., and BRANCO, J. A. (1991), "Multidimensional Scaling for N-Tuples," British Journal of Mathematical and Statistical Psychology, 44, 195-206.
9. DAWS, J. T., (1996), "The Analysis of Free-Sorting Data: Beyond Pairwise Cooccurences," Journal of Classification, 13, 57-80.
10. DE ROOIJ, M., and HEISER, W. J. (2000a), "Triadic Distance Models for the Analysis of Asymmetric Three-Way Proximity Data," British Journal of Mathematical and Statistical Psychology, 53, 99-119.
11. DE ROOIJ, M., and HEISER, W. J. (2000b), "Graphical Representations and Odds-Ratios in a Distance Association Model for the Analysis of Cross-Classified Data," Technical report, PRM-2000-01, Leiden University.
12. DENIS, J. B., and DHORNE, T. (1989), "Orthogonal Tensor Decompositions of 3-Way Tables," in Multiway Data Analysis, Eds., R. Coppi and S. Bolasco, Amsterdam: Elsevier, pp. 31-37.
13. FIENBERG, S. E. (1980), The analysis of Cross-Classified Categorical Data, Cambridge, MA: MIT press.
14. FRANC, A. (1989), "Multiway Arrays: Some Algebraic Remarks," in Multiway Data Analysis, Eds., R. Coppi and S. Bolasco, Amsterdam: Elsevier, pp. 19-29.
15. HAYASHI, C. (1972), "Two Dimensional Quantifications Based on a Measure of Dissimilarity Among Three Elements," Annals of the Institute of Statistical Mathematics, 25, 251-257.
16. HEISER, W. J., (1981), Unfolding Analysis of Proximity Data, Unpublished Doctoral Dissertation, Department of Data Theory, Leiden University.
17. HEISER, W. J., (1987), "Joint Ordination of Species and Sites: The Unfolding Technique," in Developments in Numerical Ecology, Eds., P. Legendre and L. Legendre, Berlin: Springer-Verlag, pp. 189-221.
18. HEISER, W. J. (1989), "The City-Block model for Three-Way Multidimensional Scaling," in Multiway Data Analysis, Eds., R. Coppi and S. Bolasco, Amsterdam: Elsevier, pp. 395-404.
19. HEISER, W. J., and BENNANI, M. (1997), "Triadic Distance Models: Axiomatization and Least Squares Representation," Journal of Mathematical Psychology, 41, 189-206.
20. JOLY, S., and LE CALVÉ, G. (1995), "Three-Way distances," Journal of Classification, 12, 191-205.
21. NOSOFSKY, R., (1985), "Overall Similarity and the Identification of Separable Dimension Stimuli: A Choice Model Analysis," Perception & Psychophysics, 38, 415-432.
22. OKADA, A., and IMAIZUMI, T. (1997), "Asymmetric Multidimensional Scaling of Two-Mode Three-Way Proximities," Journal of Classification, 14, 195-224.
23. PAN, G., and HARRIS, D. P. (1991), "A New Multidimensional Scaling Technique Based upon Association of Triple Objects Pijk and its Application to the Analysis of Geochemical Data," Mathematical Geology, 23, 861-886.
24. RUDAS, T., (1998), Odds Ratios in the Analysis of Contingency Tables, Newbury Park, CA: Sage.
25. SHEPARD, R. N., (1957), "Stimulus and Response Generalization: A Stochastic Model Relating Generalization to Distance in Psychological Space," Psychometrika, 22, 325-345.
26. SHEPARD, R. N., (1987), "Towards a Universal Law of Generalization for Psychological Science," Science, 237, 1317-1323.
27. TUCKER, L. R (1972), "Relations between Multidimensional Scaling and Three-Mode Factor Analysis," Psychometrika, 37, 3-27.
28. UPTON, G. J. G., (1978), The Analysis of Cross-Tabulated Data, Chichester, U.K.: Wiley.
29. VAN DER HEIJDEN, P. G. M., (1987), Correspondence Analysis of Longitudinal Data, Leiden: DSWO press.