One-Mode Multi-Way Data Analysis Using Multidimensional Scaling

本研究的目的是探讨单模式多因素多维标度（MDS）是否有必要。在以前的研究中，得出的结论是，一个模式的三路MDS的结果是类似的一个模式的两路MDS。这种相似性的原因是二元关系对三元关系的强烈影响将包括在单模式三向邻近数据中。如果单模式三向MDS的结果与单模式两向MDS的结果相似，则二元关系强烈地影响三元关系。另一方面，如果单模式三路MDS的结果与单模式二路MDS的结果不相似，则二元关系对三元关系的影响很弱。在二元关系的弱影响下，三元关系和二元关系将被分开分析。因此，本研究比较了边缘联想和条件联想的结果。考察了单模态多向多维标度模型的必要性。最后将该模型应用于消费者行为数据。

The purpose of present study is to examine whether one-mode multi-way multidimensional scaling (MDS) is necessary or not. In the previous studies, it is concluded that the results of a one-mode three-way MDS are similar to that of a one-mode two-way MDS. The reason for such similarity is that strong influences of dyadic relationships on triadic relationships would be included in one-mode three-way proximity data. If, the results of a one-mode three-way MDS are similar to that of a one-mode two-way MDS, dyadic relationships strongly influences triadic relationships. On the other hand, if the results of a one-mode three-way MDS are not similar to that of a one-mode two-way MDS, dyadic relationships weakly influences triadic relationships. Under weak influence of the dyadic relationships, the triadic and dyadic relationships would be separately analyzed. So, the present study compares the results obtained from marginal association with that of conditional association. It examined whether one-mode multi-way multidimensional scaling model is necessary or not. Finally, the proposed model was applied to the consumer behavior data.