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