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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Carroll JD, Arabie P (1980) Multidimensional scaling. In: Annual review of psychology, vol 31. Annual reviews, Palo Alto, pp 607–649
De Rooij M (2008) The analysis of change, newton’s law of gravity and association models. J R Stat Soc A (Stat Soc) 171:137–157
De Rooij M, Gower JC (2003) The geometry of triadic distances. J Classif 20(2):181–220
Gower JC, De Rooij M (2003) A comparison of the multidimensional scaling of triadic and dyadic distances. J Classif 20(1):115–136
Kruskal JB (1964a) Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29:1–27
Kruskal JB (1964b) Nonmetric multidimensional scaling: a numerical method. Psychometrika 29:115–129
Kruskal JB, Carroll JD (1969) Geometrical models and badness-of-fit functions. In: Multivariate analysis, vol 2. Academic, New York, pp 639–671
Sibson R (1978) Studies in the robustness of multidimensional scaling: procrustes statistics. J R Stat Soc B 40(2):234–238
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Nakayama, A. (2014). Analysis of Conditional and Marginal Association in One-Mode Three-Way Proximity Data. In: Gaul, W., Geyer-Schulz, A., Baba, Y., Okada, A. (eds) German-Japanese Interchange of Data Analysis Results. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-01264-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-01264-3_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01263-6
Online ISBN: 978-3-319-01264-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)