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Analysis of Conditional and Marginal Association in One-Mode Three-Way Proximity Data

Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

The purpose of this study was to examine the necessity for one-mode three-way multidimensional scaling analysis. In many cases, the results of the analysis of one-mode three-way multidimensional scaling are similar to those of one-mode two-way multidimensional scaling for lower dimensions, and, in fact, multidimensional scaling can be used for low dimensional analysis. Our results demonstrated that at lower dimensionality, triadic relationships represented by the results of one-mode three-way multidimensional scaling were almost consistent with the dyadic relationships derived from one-mode two-way multidimensional scaling. However, triadic relationships differ from dyadic relationships in analyses of higher dimensionality. The degree of coincidence obtained for one-mode three- and two-way multidimensional scaling revealed that triadic relationships can only be represented by one-mode three-way multidimensional scaling; specifically, triadic relationships based on conditional associations must be separately explained in terms of marginal associations for higher dimensionality analysis.

Notes

Acknowledgements

We would like to express our gratitude to two anonymous referees for their valuable reviews. Some parts of this research were conducted by Nakayama when he was at Nagasaki University.

References

  1. Carroll JD, Arabie P (1980) Multidimensional scaling. In: Annual review of psychology, vol 31. Annual reviews, Palo Alto, pp 607–649Google Scholar
  2. De Rooij M (2008) The analysis of change, newton’s law of gravity and association models. J R Stat Soc A (Stat Soc) 171:137–157Google Scholar
  3. De Rooij M, Gower JC (2003) The geometry of triadic distances. J Classif 20(2):181–220CrossRefMATHGoogle Scholar
  4. Gower JC, De Rooij M (2003) A comparison of the multidimensional scaling of triadic and dyadic distances. J Classif 20(1):115–136CrossRefMATHGoogle Scholar
  5. Kruskal JB (1964a) Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29:1–27MathSciNetCrossRefMATHGoogle Scholar
  6. Kruskal JB (1964b) Nonmetric multidimensional scaling: a numerical method. Psychometrika 29:115–129MathSciNetCrossRefMATHGoogle Scholar
  7. Kruskal JB, Carroll JD (1969) Geometrical models and badness-of-fit functions. In: Multivariate analysis, vol 2. Academic, New York, pp 639–671Google Scholar
  8. Sibson R (1978) Studies in the robustness of multidimensional scaling: procrustes statistics. J R Stat Soc B 40(2):234–238MathSciNetMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Tokyo Metropolitan UniversityHachioji-shiJapan

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