Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy
Wim P. Krijnen
Statistical Techniques for Applied Research
The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for indeterminate factor-error covariances to be arbitrarily small, for mean square convergence of the regression predictor of factor scores, and for the existence of a unique determinate factor and error variable. The determinate factor and error variable are uncorrelated and satisfy the defining assumptions of factor analysis. Several examples are given to illustrate the results.
Psychometrika. Vol 67(1)
common factor analysis
confirmatory factor analysis
factor indeterminacy
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Krijnen, W. P. (2006). Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy. Psychometrika. Vol 67(1), 71(3), 503-519. https://doi.org/10.1007/s11336-004-1260-2
Krijnen, Wim P. / Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy. In: Psychometrika. Vol 67(1). 2006 ; Vol. 71, No. 3. pp. 503-519.
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title = "Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy",
abstract = "The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for indeterminate factor-error covariances to be arbitrarily small, for mean square convergence of the regression predictor of factor scores, and for the existence of a unique determinate factor and error variable. The determinate factor and error variable are uncorrelated and satisfy the defining assumptions of factor analysis. Several examples are given to illustrate the results.",
keywords = "common factor analysis, confirmatory factor analysis, factor indeterminacy, factoranalyse, statistiek",
author = "Krijnen, {Wim P.}",
month = sep
journal = "Psychometrika. Vol 67(1)",
Krijnen, WP 2006, 'Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy', Psychometrika. Vol 67(1), vol. 71, no. 3, pp. 503-519. https://doi.org/10.1007/s11336-004-1260-2
Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy. / Krijnen, Wim P.
In: Psychometrika. Vol 67(1), Vol. 71, No. 3, 09.2006, p. 503-519.
T1 - Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy
AU - Krijnen, Wim P.
N2 - The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for indeterminate factor-error covariances to be arbitrarily small, for mean square convergence of the regression predictor of factor scores, and for the existence of a unique determinate factor and error variable. The determinate factor and error variable are uncorrelated and satisfy the defining assumptions of factor analysis. Several examples are given to illustrate the results.
AB - The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for indeterminate factor-error covariances to be arbitrarily small, for mean square convergence of the regression predictor of factor scores, and for the existence of a unique determinate factor and error variable. The determinate factor and error variable are uncorrelated and satisfy the defining assumptions of factor analysis. Several examples are given to illustrate the results.
KW - common factor analysis
KW - confirmatory factor analysis
KW - factor indeterminacy
KW - factoranalyse
KW - statistiek
JO - Psychometrika. Vol 67(1)
JF - Psychometrika. Vol 67(1)
Krijnen WP. Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy. Psychometrika. Vol 67(1). 2006 Sep;71(3):503-519. https://doi.org/10.1007/s11336-004-1260-2