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The Objective Definition of Simple Structure in Linear Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Ledyard R Tucker
Ledyard R Tucker*
Affiliation:
Princeton University and Educational Testing Service
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Abstract

Requirements for an objective definition of simple structure are investigated and a number of proposed objective criteria are evaluated. A distinction is drawn between exploratory factorial studies and confirmatory factorial studies, with the conclusion drawn that objective definition of simple structure depends on study design as well as on objective criteria. A proposed definition of simple structure is described in terms of linear constellations. This definition lacks only a statistical test to compare with possible chance results. A computational procedure is also described for searching for linear constellations. This procedure is very laborious and might best be accomplished on high-speed automatic computers. There is no guarantee that the procedure will find all linear constellations, but it probably would yield satisfactory results for well-designed studies.

Type
Original Paper
Information
Psychometrika , Volume 20 , Issue 3 , September 1955 , pp. 209 - 225
Copyright
Copyright © 1955 The Psychometric Society

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Footnotes

*

This research was jointly supported by Princeton University, the Office of Naval Research under contract N6onr-270-20, and the National Science Foundation under grant NSF G-642. The author is especially indebted to Harold Gulliksen for his many exceedingly helpful comments and suggestions made during the course of this development. A debt of gratitude is also owed to Mrs. Gertrude Diederich, who performed many intricate calculations in the experiments on computing procedures. The author further wishes to express his appreciation to Frederic M. Lord and David R. Saunders, who read the manuscript and made a number of very useful suggestions.

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