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Scale freeness in factor analysis

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Abstract

The notion of scale freeness does not seem to have been well understood in the factor analytic literature. It has been believed that if the loss function that is minimized to obtain estimates of the parameters in the factor model is scale invariant, then the estimates are scale free. It is shown that scale invariance of the loss function is neither a necessary nor a sufficient condition for scale freeness. A theorem that ensures scale freeness in the orthogonal factor model is given in this paper.

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Reference notes

  • McDonald, R. P., & Swaminathan, H.Structural analysis of dispersion matrices based on a very general model with a rapidly convergent procedure for the estimation of parameters. Toronto, Canada: Ontario Institute for Studies in Education, 1972.

    Google Scholar 

  • Jöreskog, K. G., Gruvaeus, G. T., & van Thillo, M.A general computer program for analysis of covariance structures (ETS RM 70-15). Princeton, N.J.: Educational Testing Service, 1970.

    Google Scholar 

References

  • Anderson, T. W.An introduction to multivariate statistics. New York: Wiley, 1958.

    Google Scholar 

  • Anderson, T. W., & Rubin, H. Statistical inference in factor analysis.Proceedings of the third Berkeley symposium on mathematical statistics and probability, 1956,V, 111–150.

    Google Scholar 

  • Harris, C. W. Some recent developments in factor analysis.Educational and Psychological Measurement, 1964,24, 193–206.

    Google Scholar 

  • Jöreskog, K. G., & Goldberger, A. S. Factor analysis by generalized least squares.Psychometrika, 1972,37, 243–260.

    Google Scholar 

  • Lawley, D. N., & Maxwell, A. E.Factor analysis as a statistical method. New York: American Elsevier Publishing Co., 1971.

    Google Scholar 

  • McDonald, R. P. A unified treatment of the weighting problem.Psychometrika, 1968,33, 351–381.

    Google Scholar 

  • McDonald, R. P. The theoretical foundations of principal factor analysis, canonical factor analysis, and alpha factor analysis.British Journal of Mathematical and Statistical Psychology, 1970,23, 1–21.

    Google Scholar 

  • Morrison, D. F.Multivariate statistical methods. New York: McGraw Hill Book Co., 1976.

    Google Scholar 

  • Press, S. J.Applied multivariate analysis. New York: Holt, Rinehart and Winston, Inc., 1972.

    Google Scholar 

  • Swain, A. J. A class of factor analysis estimation procedures with common asymptotic sampling properties.Psychometrika, 1975,40, 315–335.

    Google Scholar 

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Authors and Affiliations

  1. University of Pittsburgh, USA

    James Algina

  2. School of Education, University of Massachusetts, 01002, Amherst, MA

    Hariharan Swaminathan

Authors
  1. Hariharan Swaminathan
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  2. James Algina
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The authors are grateful for the suggestions of the referees.

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Swaminathan, H., Algina, J. Scale freeness in factor analysis. Psychometrika 43, 581–583 (1978). https://doi.org/10.1007/BF02293816

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  • DOI: https://doi.org/10.1007/BF02293816

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