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1 results

  • On the Construction of all Factors of the Model for Factor Analysis

  • Wim P. Krijnen
  • Journal:
    Psychometrika / Volume 67 / Issue 1 / March 2002
    Published online by Cambridge University Press:
    01 January 2025, pp. 161-172

  • 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 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.