Abstract
Various studies have examined multi-way proximity generalizations of multidimensional scaling (MDS). Some of these have proposed one-mode three-way proximity data analyses to investigate triadic relationships among three objects. However, the results of a triadic distance model are generally similar to those of a one-mode two-way MDS. Moreover, no technique for judging whether a triadic distance model or one-mode two-way MDS is more appropriate has been developed. Thus, it would be valuable to establish a technique for examining the need for a one-mode three-way MDS analysis. Here, we propose a technique to evaluate the need for a triadic distance model using a log-linear model. When the analysis of the log-linear model shows that three objects, i, j, and k, are not independent, the one-mode three-way proximity data should be analyzed with a triadic distance model. However, one-mode three-way proximity data should not be analyzed with a triadic distance model when the analysis of the log-linear model shows that the three objects i, j, and k are independent.
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Acknowledgements
We express our gratitude to the anonymous referees for their valuable reviews. This work was supported by a Grant-in-Aid for Young Scientists (B) (No. 25730019) from the Japan Society for the Promotion of Science.
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Nakayama, A. (2016). Evaluating the Necessity of a Triadic Distance Model. In: Wilhelm, A., Kestler, H. (eds) Analysis of Large and Complex Data. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-25226-1_17
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DOI: https://doi.org/10.1007/978-3-319-25226-1_17
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