Skip to main content
Log in

On the oblique rotation of a factor matrix to a specified pattern

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

This paper presents a procedure for rotating an arbitrary factor matrix to maximum similarity with a specified factor pattern. The sum of squared distances between specified vectors and rotated vectors in oblique Euclidian space is minimized. An example of the application of the procedure is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bargmann, R. E. Matrices and determinants. In S. M. Selby (Ed.),Handbook of tables for mathematics. (3rd ed.) Cleveland: Chemical Rubber Co., 1967. pp. 144–166.

    Google Scholar 

  • Browne, M. W. On oblique Procrustes rotation.Psychometrika, 1967,32, 125–132.

    Google Scholar 

  • Cliff, N. Orthogonal rotation to congruence.Psychomctrika, 1966,31, 33–42.

    Google Scholar 

  • Fischer, G., & Roppert, J. Bemerkungen zu einem Verfahren der Transformationsanalyse.Archiv für die gesamte Psychologie, 1964,116, 98–100.

    Google Scholar 

  • Green, B. F. The orthogonal approximation of an oblique structure in factor analysis.Psychometrika, 1952,17, 429–440.

    Google Scholar 

  • Gruvaeus, G. T. Procrustes pattern rotation. Research Bulletin. Princeton: Educational Testing Service. In preparation.

  • Guttman, L. Image theory for the structure of quantitative variates.Psychometrika, 1953,18, 277–296.

    Google Scholar 

  • Harman, H. H.Modern factor analysis. (2nd ed.) Chicago: University of Chicago Press, 1967. p. 60.

    Google Scholar 

  • Hendrickson, A. E., & White, P. O. PROMAX: A quick method for rotation to oblique simple structure.British Journal of Statistical Psychology, 1964,17, 65–70.

    Google Scholar 

  • Jennrich, R. I., & Sampson, P. F. Rotation for simple loadings.Psychometrika, 1966,31, 313–323.

    Google Scholar 

  • Kaiser, H. F. Image analysis. In C. W. Harris (Ed.),Problems in measuring change. University of Wisconsin Press, 1963.

  • Kristof, W. Die beste orthogonale Transformation zur gegenseitigen Überführung zweier Faktorenmatrizen.Diagnostica, 1964,10, 87–90.

    Google Scholar 

  • Meredith, W. Notes on factorial invariance.Psychometrika, 1964,29, 177–185.

    Google Scholar 

  • Mosier, C. I. Determining a simple structure when loadings for certain tests are known.Psychometrika, 1939,4, 149–192.

    Google Scholar 

  • Schönemann, P. H. A generalized solution of the orthogonal Procrustes problem.Psychometrika, 1966,31, 1–10.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported in part by the National Institute of Child Health and Human Development, Research Grant 1 PO1 HDO1762.

The names of the authors are given in alphabetical order. Their contributions to the paper are equal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Browne, M., Kristof, W. On the oblique rotation of a factor matrix to a specified pattern. Psychometrika 34, 237–248 (1969). https://doi.org/10.1007/BF02289347

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02289347

Keywords

Navigation