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

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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 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.

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Authors and Affiliations

  1. Developmental Psychology, University of Amsterdam, Roetersstraat 15, 1018 WB, Amsterdam, The Netherlands

    Wim P. Krijnen

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  1. Wim P. Krijnen
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Correspondence to Wim P. Krijnen.

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I would like to thank Willem Schaafsma for useful discussions pertaining to the model for factor analysis. I am indebted to Peter Molenaar and Conor Dolan for their comments on the manuscript. Additionally, I thank the reviewers for the constructive remarks on an earlier draft of the paper.

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Krijnen, W.P. On the construction of all factors of the model for factor analysis. Psychometrika 67, 161–172 (2002). https://doi.org/10.1007/BF02294714

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  • DOI: https://doi.org/10.1007/BF02294714

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