, Volume 31, Issue 3, pp 279-311

Some mathematical notes on three-mode factor analysis

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Abstract

The model for three-mode factor analysis is discussed in terms of newer applications of mathematical processes including a type of matrix process termed the Kronecker product and the definition of combination variables. Three methods of analysis to a type of extension of principal components analysis are discussed. Methods II and III are applicable to analysis of data collected for a large sample of individuals. An extension of the model is described in which allowance is made for unique variance for each combination variable when the data are collected for a large sample of individuals.

This research was jointly supported by the University of Illinois and the Office of Naval Research under contract Nonr 1834 (39). The author is most appreciative of the careful reading of the manuscript by Dr. Douglas McKie and Dr. Maurice Tatsuoka.