Psychometrika (2006) 71(3) 503-519

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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. © 2006 The Psychometric Society.

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Krijnen, W. P. (2006). Implications of indeterminate factor-error covariances for factor construction, prediction, and determinacy. *Psychometrika*, *71*(3), 503–519. https://doi.org/10.1007/s11336-004-1260-2

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