Behaviormetrika
Online ISSN : 1349-6964
Print ISSN : 0385-7417
ISSN-L : 0385-7417
QUASI THREE-MODE PRINCIPAL COMPONENT ANALYSIS —A METHOD FOR ASSESSING THE FACTOR CHANGE—
Takashi Murakami
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1983 Volume 10 Issue 14 Pages 27-48

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Abstract

This paper describes an exploratory procedure for assessing the factor change, quasi three-mode factor analysis, which is applicable to longitudinal or multitraitmultimethod data. The model is a simplified case of Tucker's three-mode factor analysis, and formally equivalent to Kroonenberg and de Leeuw's Tucker 2 model. That is, it intends to decompose the standardized data matrix for each occasion into the product of three matrices, namely, the factor score matrix, the core matrix, and the factor loading matrix. It is illustrated that the patterns to which core matrices conform can distinguish the change of factor loadings from the change of factor scores. A practical least squares algorithm for the model is formulated, and a way of scalings of parameters which facilitates the interpretation of the results and the comparison with the output of other factor analytic methods is discussed. Analysis of a multitrait-multimethod matrix is attached as a numerical example.

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