Nonmetric three-mode principal component analysis for qualitative data

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  • 質的データに対する非計量三相主成分分析法
  • シツテキ データ ニ タイスル ヒケイリョウ サンソウ シュセイブン ブンセキホウ

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Abstract

TUCKER3 (Tucker, 1966) is one of the methods of principal component analysis (PCA) for “quantitative” three-mode data. In this paper,we extend TUCKER3 to “nonmetric” three-mode PCA by deriving quantification scores. We also present an alternating least squares algorithm for finding optimal solution of nonmetric three-mode PCA by updating parameters such as quantification scores, loading matrices and core matrix successively. Calculating quantification scores of qualitative variables allows us to exclude arbitrariness which is included in questionnaire, such as the coding of nominal variables and the equality of intervals of ordinal variables. Two real data examples are given to illustrate the effectiveness of the proposed procedure.

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