Convergence in mean square of factor predictors.

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Sufficient conditions for mean square convergence of factor predictors in common factor analysis are given by Guttman, by Williams, and by Schneeweiss and Mathes. These conditions do not hold for confirmatory factor analysis or when an error variance equals zero (Heywood cases). Two sufficient conditions are given for the three basic factor predictors and a predictor from rotated principal components analysis to converge to the factors of the model for confirmatory factor analysis, including Heywood cases. For certain model specifications the conditions are necessary. The conditions are sufficient for the existence of a unique true factor. A geometric interpretation is given for factor indeterminacy and mean square convergence of best linear factor prediction.
Original languageEnglish
Pages (from-to)311-326
JournalThe British journal of mathematical and statistical psychology
Volume57
Issue numberPt 2
DOIs
Publication statusPublished - 2004

Keywords

  • statistics
  • models, theoretical
  • psychology

Cite this

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abstract = "Sufficient conditions for mean square convergence of factor predictors in common factor analysis are given by Guttman, by Williams, and by Schneeweiss and Mathes. These conditions do not hold for confirmatory factor analysis or when an error variance equals zero (Heywood cases). Two sufficient conditions are given for the three basic factor predictors and a predictor from rotated principal components analysis to converge to the factors of the model for confirmatory factor analysis, including Heywood cases. For certain model specifications the conditions are necessary. The conditions are sufficient for the existence of a unique true factor. A geometric interpretation is given for factor indeterminacy and mean square convergence of best linear factor prediction.",
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author = "Krijnen, {Wim P}",
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pages = "311--326",
journal = "The British journal of mathematical and statistical psychology",
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Convergence in mean square of factor predictors. / Krijnen, Wim P.

In: The British journal of mathematical and statistical psychology, Vol. 57, No. Pt 2, 2004, p. 311-326.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - Sufficient conditions for mean square convergence of factor predictors in common factor analysis are given by Guttman, by Williams, and by Schneeweiss and Mathes. These conditions do not hold for confirmatory factor analysis or when an error variance equals zero (Heywood cases). Two sufficient conditions are given for the three basic factor predictors and a predictor from rotated principal components analysis to converge to the factors of the model for confirmatory factor analysis, including Heywood cases. For certain model specifications the conditions are necessary. The conditions are sufficient for the existence of a unique true factor. A geometric interpretation is given for factor indeterminacy and mean square convergence of best linear factor prediction.

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KW - models, theoretical

KW - psychology

KW - psychologie

KW - statistiek

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EP - 326

JO - The British journal of mathematical and statistical psychology

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