Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric


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.

This is a preview of subscription content, access via your institution.


  1. Anderson, T.W. (1984). An introduction to multivariate statistical analysis. New York: Wiley.

    Google Scholar 

  2. Asparouhov, T., & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16, 397–438.

    Article  Google Scholar 

  3. Bekker, P.A., Merckens, A., & Wansbeek, T.J. (1994). Identification, equivalent models, and computer algebra. Boston: Academic Press.

    Google Scholar 

  4. Bollen, K.A., & Jöreskog, K.G. (1985). Uniqueness does not imply identification: A note on confirmatory factor analysis. Sociological Methods and Research, 14, 155–163.

    Article  Google Scholar 

  5. Dolan, C.V., & Molenaar, P.C.M. (1991). A comparison of four methods of calculating standard errors of maximum-likelihood estimates in the analysis of covariance structure. British Journal of Mathematical and Statistical Psychology, 44, 359–368.

    Article  Google Scholar 

  6. Dunn, J.E. (1973). A note on a sufficiency condition for uniqueness of a restricted factor matrix. Psychometrika, 38, 141–143.

    Article  Google Scholar 

  7. Geweke, J.F., & Zhou, G. (1996). Measuring the pricing error of the arbitrage pricing theory. Review of Financial Studies, 9, 557–587.

    Article  Google Scholar 

  8. Howe, W.G. (1955). Some contributions to factor analysis (Tech. Rep. No. ORNL-1919). Oak Ridge, Tennessee: Oak Ridge National Laboratory.

  9. Hoyle, R.H., & Duvall, J.L. (2004). Determining the number of factors in exploratory and confirmatory factor analysis. In D. Kaplan (Ed.), The SAGE handbook of quantitative methodology for the social sciences (pp. 301–315). Thousand Oaks: SAGE.

    Google Scholar 

  10. Jennrich, R.I. (1978). Rotational equivalence of factor loading matrices with specified values. Psychometrika, 43, 421–426.

    Article  Google Scholar 

  11. Jöreskog, K.G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183–202.

    Article  Google Scholar 

  12. Jöreskog, K.G. (1979). Author’s addendum. In J. Magidson (Ed.), Advances in factor analysis and structural equation models (pp. 40–43). Cambridge: Abt Books.

    Google Scholar 

  13. Mulaik, S.A. (2010). Foundations of factor analysis (2nd ed.). Boca Raton: Chapman and Hall/CRC.

    Google Scholar 

Download references


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.

Author information



Corresponding author

Correspondence to Carel F. W. Peeters.

Additional information

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.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Peeters, C.F.W. Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric. Psychometrika 77, 288–292 (2012).

Download citation

Key words

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