Conditions for factor (in)determinacy in factor analysis

Wim P. Krijnen, Theo K. Dijkstra, Richard D. Gill

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)359-367
JournalPsychometrika. Vol 67(1)
Volume63
Issue number4
DOIs
Publication statusPublished - Dec 1998

Keywords

  • factor analysis

Cite this

Krijnen, Wim P. ; Dijkstra, Theo K. ; Gill, Richard D. / Conditions for factor (in)determinacy in factor analysis. In: Psychometrika. Vol 67(1). 1998 ; Vol. 63, No. 4. pp. 359-367.
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Conditions for factor (in)determinacy in factor analysis. / Krijnen, Wim P.; Dijkstra, Theo K.; Gill, Richard D.

In: Psychometrika. Vol 67(1), Vol. 63, No. 4, 12.1998, p. 359-367.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - 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.

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