The orthogonal approximation of an oblique structure in factor analysis
- 365 Downloads
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.
KeywordsPublic Policy Statistical Theory Factor Matrix Orthogonal Transformation Orthogonal Vector
Unable to display preview. Download preview PDF.
- 1.Aitken, A. C. Determinants and matrices. Edinburgh: Oliver and Boyd, 1942.Google Scholar
- 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 Unpublished Ed.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.Dwyer, P. S. The contribution of an orthogonal multiple factor solution to multiple correlation.Psychometrika, 1939,4, 163–171.Google Scholar
- 4.Dwyer, P. S. Linear computations. New York: John Wiley and Sons, 1951.Google Scholar
- 5.Gibson, W. Orthogonal and oblique simple structures.Psychometrika, 1952,17, 317–323.Google Scholar
- 6.Guilford, J. P., and Michael, W. B. Approaches to univocal factor scores.Psychometrika, 1948,13, 1–22.Google Scholar
- 7.Guttman, L. Multiple rectilinear regression and the resolution into components.Psychometrika, 1940,5, 75–100.Google Scholar
- 8.Mosier, C. I. Determining a simple structure when loadings for certain tests are known.Psychometrika, 1939,4, 149–162.Google Scholar
- 9.Roff, M. Some properties of the communality in multiple factor theory.Psycho-metrika, 1936,1, 1–6.Google Scholar
- 10.Tucker, L. R. The role of correlated factors in factor analysis.Psychometrika, 1940,5, 141–152.Google Scholar
- 11.Thurstone, L. L. Multiple-factor analysis. Chicago: Univ. Chicago Press, 1947.Google Scholar