Tucker2 as a Second-order Principal Component Analysis
Statistical properties of the Tucker2 (T2) model, a simplified version of three-mode principal component analysis (PCA), are investigated aiming at applications to the study of factor invariance. The T2 model is derived as a restricted form of second-order PCA in the situation comparing component loadings and component scores across occasions. Several statistical interpretations of coefficients obtained from the least squares algorithm of T2 are proposed, and several aspects of T2 are shown to be natural extensions of characteristics of classical PCA. A scale free formulation of T2 and a new derivation of the algorithm for the large sample case are also shown. The relationship with a generalized canonical correlation model is suggested.
KeywordsSingular Value Decomposition Component Score Orthogonal Rotation Pattern Matrix Asymmetric Role
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