Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric

Abstract

In an addendum to his seminal 1969 article Jöreskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix (Jöreskog in Advances in factor analysis and structural equation models, pp. 40–43, 1979). These condition sets, formulated under factor correlation and factor covariance metrics, respectively, were claimed to be equivalent and to lead to global rotational uniqueness of the factor solution. It is shown here that the conditions for the oblique factor correlation structure need to be amended for global rotational uniqueness, and, hence, that the condition sets are not equivalent in terms of unicity of the solution.

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Acknowledgements

This research was supported by grant NWO-VICI-453-05-002 of the Netherlands Organization for Scientific Research (NWO). The author would like to thank the Editor, Associate Editor, and two anonymous reviewers for constructive comments.

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Correspondence to Carel F. W. Peeters.

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Written while a Ph.D. candidate at the Department of Methodology and Statistics, Utrecht University, Utrecht, the Netherlands. Starting February 1, the author will be at the Department of Epidemiology & Biostatistics, VU University medical center, Amsterdam, the Netherlands.

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Peeters, C.F.W. Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric. Psychometrika 77, 288–292 (2012). https://doi.org/10.1007/s11336-012-9259-3

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Key words

  • factor analysis
  • oblique rotation
  • rotational uniqueness
  • unrestricted factor model