Conditions for factor (in)determinacy in factor analysis

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

doi:10.1007/BF02294860

Conditions for factor (in)determinacy in factor analysis

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

Statistical Techniques for Applied Research

Research output: Contribution to journal › Article › Academic › peer-review

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 language	English
Pages (from-to)	359-367
Journal	Psychometrika. Vol 67(1)
Volume	63
Issue number	4
DOIs	https://doi.org/10.1007/BF02294860
Publication status	Published - Dec 1998

Keywords

factor analysis

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10.1007/BF02294860

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title = "Conditions for factor (in)determinacy in factor analysis",

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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author = "Krijnen, {Wim P.} and Dijkstra, {Theo K.} and Gill, {Richard D.}",

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T1 - Conditions for factor (in)determinacy in factor analysis

AU - Krijnen, Wim P.

AU - Dijkstra, Theo K.

AU - Gill, Richard D.

PY - 1998/12

Y1 - 1998/12

N2 - 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.

AB - 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.

KW - factor analysis

KW - factoranalyse

U2 - 10.1007/BF02294860

DO - 10.1007/BF02294860

M3 - Article

SN - 0033-3123

VL - 63

SP - 359

EP - 367

JO - Psychometrika. Vol 67(1)

JF - Psychometrika. Vol 67(1)

IS - 4

ER -

Conditions for factor (in)determinacy in factor analysis

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Keywords

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