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The Extension of Component Analysis to Four-Mode Matrices

Published online by Cambridge University Press:  01 January 2025

John L. Lastovicka
John L. Lastovicka*
Affiliation:
University of Kansas
*
Requests for reprints and copies of raw data upon which the reported analysis is based should be sent to John L. Lastovicka, School of Business, University of Kansas, Lawrence, Kansas 66045.
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Abstract

A model for four-mode component analysis is developed and presented. The developed model, which is an extension of Tucker's three-mode factor analytic model, allows for the simultaneous analysis of all modes of a four-mode data matrix and the consideration of relationships among the modes. An empirical example based upon viewer perceptions of repetitive advertising shows the four-mode model applicable to real data.

Keywords

advertisingcomponent analysisfactor analysisfour-mode modelsthree-mode models
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 1 , March 1981 , pp. 47 - 57
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

This research was supported by the University of Kansas School of Business Research Fund provided by the Fourth National Bank & Trust Company, Wichita. The ideas and opinions expressed herein are solely those of the author.

The author acknowledges with thanks Deborah A. Aycox, for collecting the data analyzed in the empirical example, and John S. Brennan, for writing matrix algebra computer subroutines used to perform the data analysis.

References

Reference Note

Manual for the Leo Burnett storyboard test-system. Chicago, Ill.: Leo Burnett Company, Inc., 1977.Google Scholar

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