2次合成変量のアルファ係数の和を最大化する多集合データの階層的主成分分析I

概要

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A component analytical model treating the several sets of variables is proposed in this paper. The model has the hierarchical property; The first order composites are defined as linear combinations of variables for each set, and the second order composites are constructed as linear combinations of the first order ones of all the sets. The optimization criterion is the maximization of the sum of alpha coefficients of the second order composites. The model may be regarded as a natural extension of the ordinary component analysis in Lord's(1958) sense. Through changing the number of the second order composites, the first order composites could be explored in such a way that the latter would be well be well balanced between the internal consistency coefficients and the correlations between the sets. For this study, an alternating optimization algorithm of the model was formulated as a first part, but the need for examining relationship with other models and demonstrating numerical examples based on this model was stressed for the next study.
経営行動科学学会の論文
1987-04-15