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A Note on Approximation of Likelihood Ratio Statistic in Exploratory Factor Analysis

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DOI: 10.4236/ojs.2015.56061    2,180 Downloads   2,587 Views   Citations


In normal theory exploratory factor analysis, likelihood ratio (LR) statistic plays an important role in evaluating the goodness-of-fit of the model. In this paper, we derive an approximation of the LR statistic. The approximation is then used to show explicitly that the expectation of the LR statistic agrees with the degrees of freedom of the asymptotic chi-square distribution.

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The authors declare no conflicts of interest.

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Ichikawa, M. (2015) A Note on Approximation of Likelihood Ratio Statistic in Exploratory Factor Analysis. Open Journal of Statistics, 5, 600-603. doi: 10.4236/ojs.2015.56061.


[1] Anderson, T.W. (2003) An Introduction to Multivariate Statistical Analysis. 3rd Edition, John Wiley & Sons, Hoboken.
[2] Lawley, D.N. and Maxwell, A.E. (1971) Factor Analysis as a Statistical Method. 2nd Edition, Butterworths, London.
[3] Anderson, T.W. and Rubin, H. (1956) Statistical Inference in Factor Analysis. In: Neyman, J., Ed., Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, Vol. 5, Berkeley, 111-150.
[4] Browne, M.W., MacCallum, R.C., Kim, C.-T., Andersen, B.L. and Gleser, R. (2002) When Fit Indices and Residuals are Incompatible. Psychological Methods, 7, 403-421.
[5] Horn, R.A. and Johnson, C.R. (1991) Topics in Matrix Analysis. Cambridge University Press, Cambridge.
[6] Ichikawa, M. and Konishi, S. (2002) Asymptotic Expansions and Bootstrap Approximations in Factor Analysis. Journal of Multivariate Analysis, 81, 47-66.

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