On the construction of all factors of the model for factor analysis.

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

A construction method is given for all factors that satisfy the assumptions of the model for factor analysis, including partially determined factors where certain error variances are zero. Various criteria for the seriousness of indeterminacy are related. It is shown that B. F. Green's (1976) conjecture holds: For a linear factor predictor the mean squared error of prediction is constant over all possible factors. A simple and general geometric interpretation of factor indeterminacy is given on the basis of the distance between multiple factors. It is illustrated that variable elimination can have a large effect on the seriousness of factor indeterminacy. A simulation study reveals that if the mean square error of factor prediction equals .5, then two thirds of the persons are "correctly" selected by the best linear factor predictor. (PsycINFO Database Record (c) 2009 APA, all rights reserved)
Original languageEnglish
Pages (from-to)161-172
Number of pages12
JournalPsychometrika. Vol 67(1)
Volume67
Issue number1
DOIs
Publication statusPublished - Mar 2002

Keywords

  • indeterminacy
  • factor scores
  • Confirmatory factor analysis
  • exploratory factor analysis
  • distance between factors

Cite this

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On the construction of all factors of the model for factor analysis. / Krijnen, Wim P.

In: Psychometrika. Vol 67(1), Vol. 67, No. 1, 03.2002, p. 161-172.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - A construction method is given for all factors that satisfy the assumptions of the model for factor analysis, including partially determined factors where certain error variances are zero. Various criteria for the seriousness of indeterminacy are related. It is shown that B. F. Green's (1976) conjecture holds: For a linear factor predictor the mean squared error of prediction is constant over all possible factors. A simple and general geometric interpretation of factor indeterminacy is given on the basis of the distance between multiple factors. It is illustrated that variable elimination can have a large effect on the seriousness of factor indeterminacy. A simulation study reveals that if the mean square error of factor prediction equals .5, then two thirds of the persons are "correctly" selected by the best linear factor predictor. (PsycINFO Database Record (c) 2009 APA, all rights reserved)

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