Abstract
This chapter discusses the correlation analysis of n-way qualitative data. The latent structure of n-way qualitative data by observing Euclidean configurations of the elements has been investigated by using the obtained scores. Therefore, it depends upon the choice of object function whether the unknown structure can be extracted by applying the optimal scoring method to a given n-way qualitative data. However, it is difficult to determine the most appropriate object function because the structure of a given data is unknown in advance. A new method for n-way qualitative data has been proposed and has been applied to the real 3-way qualitative data of the general elections in Japan. The optimal scoring method for n-way qualitative data has also been proposed under the criterion of maximizing multiple correlation coefficients. One of the generalizations of correspondence analysis to n-way qualitative data has also been introduced. The singular value decomposition of multi-way contingency table has been scrutinized. The chapter discusses the optimal scoring method under the criterion of maximization of canonical correlation.
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