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A maximum likelihood method for an asymmetric MDS model

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  • Saburi, S.
  • Chino, N.

Abstract

A maximum likelihood estimation method is proposed to fit an asymmetric multidimensional scaling model to a set of asymmetric data. This method is based on successive categories scaling, and enables us to analyze asymmetric proximity data measured, at least, at an ordinal scale level. It enables us to examine not only the appropriate scaling level of the data, but also the appropriate dimensionality of the model, using AIC. Prior to or in fitting the asymmetric MDS model, it is important to verify that the data are sufficiently asymmetric. Some variants of symmetry hypotheses are developed for this purpose. Since the emphasis in our paper is not on hypothesis testing, but on model diagnosis, we compare several candidate models including models with these hypotheses based on a similar model comparison idea using AIC. The method is applied to artificial data and a set of friendship data among nations in East Asia and the USA. Relations to other methods are also discussed.

Suggested Citation

  • Saburi, S. & Chino, N., 2008. "A maximum likelihood method for an asymmetric MDS model," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4673-4684, June.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4673-4684
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    1. J. Ramsay, 1980. "Some small sample results for maximum likelihood estimation in multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 139-144, March.
    2. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    3. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
    4. Townsend, James T. & Landon, Douglas E., 1983. "Mathematical models of recognition and confusion in psychology," Mathematical Social Sciences, Elsevier, vol. 4(1), pages 25-71, February.
    5. Richard A. Harshman & Paul E. Green & Yoram Wind & Margaret E. Lundy, 1982. "A Model for the Analysis of Asymmetric Data in Marketing Research," Marketing Science, INFORMS, vol. 1(2), pages 205-242.
    6. David Weeks & P. Bentler, 1982. "Restricted multidimensional scaling models for asymmetric proximities," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 201-208, June.
    7. Peter Schönemann & Robert Carroll, 1970. "Fitting one matrix to another under choice of a central dilation and a rigid motion," Psychometrika, Springer;The Psychometric Society, vol. 35(2), pages 245-255, June.
    8. A. G. Constantine & J. C. Gower, 1978. "Graphical Representation of Asymmetric Matrices," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 297-304, November.
    9. Suzanne Winsberg & J. Douglas Carroll, 1989. "A quasi-nonmetric method for multidimensional scaling VIA an extended euclidean model," Psychometrika, Springer;The Psychometric Society, vol. 54(2), pages 217-229, June.
    10. Campbell Read, 1978. "Tests of symmetry in three-way contingency tables," Psychometrika, Springer;The Psychometric Society, vol. 43(3), pages 409-420, September.
    11. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    12. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    13. Mark Rooij & Willem Heiser, 2005. "Graphical representations and odds ratios in a distance-association model for the analysis of cross-classified data," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 99-122, March.
    14. Henk Kiers & Yoshio Takane, 1994. "A generalization of GIPSCAL for the analysis of nonsymmetric data," Journal of Classification, Springer;The Classification Society, vol. 11(1), pages 79-99, March.
    15. Akinori Okada & Tadashi Imaizumi, 1997. "Asymmetric multidimensional scaling of two-mode three-way proximities," Journal of Classification, Springer;The Classification Society, vol. 14(2), pages 195-224, September.
    16. Jan Leeuw & Jacqueline Meulman, 1986. "A special Jackknife for Multidimensional Scaling," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 97-112, March.
    17. ten Berge, Jos M. F., 1997. "Reduction of asymmetry by rank-one matrices," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 357-366, May.
    18. Yoshio Takane, 1981. "Multidimensional successive categories scaling: A maximum likelihood method," Psychometrika, Springer;The Psychometric Society, vol. 46(1), pages 9-28, March.
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