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Quadratic Prediction of Factor Scores

Published online by Cambridge University Press:  01 January 2025

Erik Meijer  and
Tom Wansbeek
Erik Meijer*
Affiliation:
Department of Econometrics, University of Groningen
Tom Wansbeek
Affiliation:
Department of Econometrics, University of Groningen
*
Requests for reprints should be sent to Erik Meijer, University of Groningen, Department of Econometrics, P.O. Box 800, 9700 AV Groningen, THE NETHERLANDS. E-mail: [email protected]
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Abstract

Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. It is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic function of y.

Keywords

factor scoresnonnormalityefficiency
Type
Report
Information
Psychometrika , Volume 64 , Issue 4 , December 1999 , pp. 495 - 507
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

The authors would like to thank Edith Nijenhuis, the anonymous referees, and the associate editor for their helpful comments and suggestions.

References

Aitken, A. C. (1935). On least squares and linear combinations of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.CrossRefGoogle Scholar
Cramér, H. (1946). Mathematical methods of statistics, Princeton: Princeton University Press.Google Scholar
Hsiao, C. (1992). Nonlinear latent variable models. In Mátyás, L., & Sevestre, P. (Eds.), The econometrics of panel data (pp. 429–448). Dordrecht: Kluwer.Google Scholar
Koning, R. H., Neudecker, H., & Wansbeek, T. J. (1992). Unbiased estimation of fourth-order matrix moments. Linear Algebra and its Applications, 160, 163–174.CrossRefGoogle Scholar
Krijnen, W. P., Wansbeek, T. J., & ten Berge, J. M. F. (1996). Best linear predictors for factor scores. Communications in Statistics — Theory and Methods, 25, 3013–3025.CrossRefGoogle Scholar
Magnus, J. R. (1988). Linear structures, London: Griffin.Google Scholar
Magnus, J. R., & Neudecker, H. (1988). Matrix differential calculus with applications in statistics and econometrics, Chichester: Wiley.Google Scholar
McGaw, B., & Jöreskog, K. G. (1971). Factorial invariance of ability measures in groups differing in intelligence and socioeconomic status. British Journal of Mathematical and Statistical Psychology, 24, 154–168.CrossRefGoogle Scholar
Mei, J. (1993). A semiautoregressive approach to the arbitrage price theory. The Journal of Finance, 48, 599–620.CrossRefGoogle Scholar
Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156–166.CrossRefGoogle Scholar
ten Berge, J. M. F., Krijnen, W. P., Wansbeek, T. J., & Shapiro, A. (1999). Some new results on correlation preserving factor scores prediction methods. Linear Algebra and its Applications, 289, 311–318.CrossRefGoogle Scholar
Thurstone, L. L. (1935). The vectors of mind, Chicago: University of Chicago Press.Google Scholar
Wansbeek, T. J. (1989). Permutation matrix —II. In Kotz, S., & Johnson, N. L. (Eds.), Encyclopedia of statistical sciences, supplement volume (pp. 121–122). New York: Wiley.Google Scholar