多変量解析諸手法のモデル再現性に関する数値実験

Abstract

A series of experiments on the model-reproducibility of some procedures in multivariate analysis was carried out in this paper. The following five procedures were dealt with: Hayashi's third method of quantification, categorical canonical correlation analysis, factor analysis(centroid method and least-squares method)and principal component analysis. They share the feature of having the objective of analyzing the inner correlations without so-called outside variables. The original model is a plane figure consisting of two circles with sixteen points representing individuals and five points representing categories. Measurement of the linear distances between the two groups of points gives rise to a data matrix of size16×5. Each of the five procedures was used to analyze the data matrix and then to draw the scatter plots of individuals and categories. Using the closeness of the scatter plots with the original figure, the procedures were ranked from the worst to best in the previous order with the last two tied. It is proved also that if the data matrix consists of squared distances, then the principal component analysis leads to a faithful representation of the original figure.