# Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy

### Uittreksel

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.
Originele taal-2 English 503-519 Psychometrika. Vol 67(1) 71 3 https://doi.org/10.1007/s11336-004-1260-2 Published - sep 2006

### Vingerafdruk

Determinacy
Statistical Factor Analysis
Factor analysis
Prediction
Factor Analysis
Mean-square Convergence
Predictors
Regression
Necessary Conditions
Sufficient Conditions
Model

### Keywords

• factoranalyse
• statistiek

### Citeer dit

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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.}",
year = "2006",
month = "9",
doi = "10.1007/s11336-004-1260-2",
language = "English",
volume = "71",
pages = "503--519",
journal = "Psychometrika. Vol 67(1)",
issn = "0033-3123",
publisher = "Springer Verlag",
number = "3",

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In: Psychometrika. Vol 67(1), Vol. 71, Nr. 3, 09.2006, blz. 503-519.

TY - JOUR

T1 - Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy

AU - Krijnen, Wim P.

PY - 2006/9

Y1 - 2006/9

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

U2 - 10.1007/s11336-004-1260-2

DO - 10.1007/s11336-004-1260-2

M3 - Article

VL - 71

SP - 503

EP - 519

JO - Psychometrika. Vol 67(1)

JF - Psychometrika. Vol 67(1)

SN - 0033-3123

IS - 3

ER -