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Conditions for Factor (in)Determinacy in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Wim P. Krijnen ,
Theo K. Dijkstra  and
Richard D. Gill
Wim P. Krijnen*
Affiliation:
University of Groningen
Theo K. Dijkstra
Affiliation:
University of Groningen
Richard D. Gill
Affiliation:
University of Utrecht
*
Requests for reprints should be sent to Wim P. Krijnen, Lisdodde I, 9679 MC Scheemda, THE NETHERLANDS.
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Abstract

The subject of factor indeterminacy has a vast history in factor analysis (Guttman, 1955; Lederman, 1938; Wilson, 1928). It has lead to strong differences in opinion (Steiger, 1979). The current paper gives necessary and sufficient conditions for observability of factors in terms of the parameter matrices and a finite number of variables. Five conditions are given which rigorously define indeterminacy. It is shown that (un)observable factors are (in)determinate. Specifically, the indeterminacy proof by Guttman is extended to Heywood cases. The results are illustrated by two examples and implications for indeterminacy are discussed.

Keywords

indeterminacyHeywood casesmean squared errorfactor score prediction
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 4 , December 1998 , pp. 359 - 367
Copyright
Copyright © 1998 The Psychometric Society

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