Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-08T07:54:39.488Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Mathematical Notes on Three-Mode Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Ledyard R Tucker
Ledyard R Tucker*
Affiliation:
University of Illinois
Get access Rights & Permissions [Opens in a new window]

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.

Information

Type
Original Paper
Information
Psychometrika , Volume 31 , Issue 3 , September 1966 , pp. 279 - 311
Copyright
Copyright © 1966 Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

*

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.

References

Bellman, R. R. Introduction to matrix analysis, New York: McGraw-Hill, 1960.Google Scholar
Campbell, D. T. and Fiske, D. W. Convergent and discriminant validation by the multitrait-multimethod matrix. Psychol. Bull., 1959, 56, 81–105.10.1037/h0046016CrossRefGoogle ScholarPubMed
Eckart, C. and Young, G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218.10.1007/BF02288367CrossRefGoogle Scholar
Levin, J. Three-mode factor analysis. Tech. Rept., Dept. Psychol., Univ. Ill., 1963.Google Scholar
Levin, J. Three-mode factor analysis. Psychol. Bull., 1965, 64, 442–452.10.1037/h0022603CrossRefGoogle ScholarPubMed
MacDuffee, C. C. The theory of matrices, New York: Chelsea, 1946.Google Scholar
Osgood, C. E., Suci, G. J., and Tannenbaum, P. H. The measurement of meaning, Urbana, Illinois: Univ. Ill. Press, 1957.Google Scholar
Tucker, L. R. Implications of factor analysis of three-way matrices for measurement of change. In Harris, C. W. (Eds.), Problems in measuring change. Madison, Wis.: Univ. Wis. Press, 1963, 122–137.Google Scholar
Tucker, L. R. The extension of factor analysis to three-dimensional matrices. In Frederiksen, N. and Gulliksen, H. (Eds.), Contributions to mathematical psychology. New York: Holt, Rinehart and Winston, 1964, 109–127.Google Scholar
Tucker, L. R. Experiments in multi-mode factor analysis. Proceedings of the 1964 Invitational Conference on Testing Problems. Princeton, N. J.: Educ. Test. Serv., 1965, 46–57.Google Scholar