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

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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.
Original languageEnglish
Pages (from-to)503-519
JournalPsychometrika. Vol 67(1)
Issue number3
Publication statusPublished - Sep 2006



  • common factor analysis
  • confirmatory factor analysis
  • factor indeterminacy

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