, Volume 17, Issue 4, pp 429–440 | Cite as

The orthogonal approximation of an oblique structure in factor analysis

  • Bert F. Green


A procedure is derived for obtaining an orthogonal transformation which most nearly transforms one given matrix into another given matrix, according to some least-squares criterion of fit. From this procedure, three analytic methods are derived for obtaining an orthogonal factor matrix which closely approximates a given oblique factor matrix. The case is considered of approximating a specified subset of oblique vectors by orthogonal vectors.


Public Policy Statistical Theory Factor Matrix Orthogonal Transformation Orthogonal Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Aitken, A. C. Determinants and matrices. Edinburgh: Oliver and Boyd, 1942.Google Scholar
  2. 2.
    Bryan, J. G. A method for the exact determination of the characteristic equation and latent vectors of a matrix with applications to the discriminant function for more than two groups. Unpublished Ed. D. Thesis, Graduate School of Education, Harvard University, 1950.Google Scholar
  3. 3.
    Dwyer, P. S. The contribution of an orthogonal multiple factor solution to multiple correlation.Psychometrika, 1939,4, 163–171.Google Scholar
  4. 4.
    Dwyer, P. S. Linear computations. New York: John Wiley and Sons, 1951.Google Scholar
  5. 5.
    Gibson, W. Orthogonal and oblique simple structures.Psychometrika, 1952,17, 317–323.Google Scholar
  6. 6.
    Guilford, J. P., and Michael, W. B. Approaches to univocal factor scores.Psychometrika, 1948,13, 1–22.Google Scholar
  7. 7.
    Guttman, L. Multiple rectilinear regression and the resolution into components.Psychometrika, 1940,5, 75–100.Google Scholar
  8. 8.
    Mosier, C. I. Determining a simple structure when loadings for certain tests are known.Psychometrika, 1939,4, 149–162.Google Scholar
  9. 9.
    Roff, M. Some properties of the communality in multiple factor theory.Psycho-metrika, 1936,1, 1–6.Google Scholar
  10. 10.
    Tucker, L. R. The role of correlated factors in factor analysis.Psychometrika, 1940,5, 141–152.Google Scholar
  11. 11.
    Thurstone, L. L. Multiple-factor analysis. Chicago: Univ. Chicago Press, 1947.Google Scholar

Copyright information

© Psychometric Society 1952

Authors and Affiliations

  • Bert F. Green
    • 1
  1. 1.Massachusetts Institute of TechnologyUSA

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