Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-08T09:53:25.908Z Has data issue: false hasContentIssue false

A Note on Factor Analysis: Arbitrary Orthogonal Transformations

Published online by Cambridge University Press:  01 January 2025

Edward E. Cureton*
Affiliation:
University of Tennessee

Abstract

A modification of the Gram-Schmidt process yields an easily constructed orthogonal transformation matrix which may be used to rotate a centroid, principal axis, or maximum likelihood factor matrix in a manner such that one of the new axes has predetermined direction. The procedure is illustrated by rotating a centroid factor matrix into an abbreviated bifactor matrix, the general factor being defined as the centroid of a specified subgroup of reasoning tests.

Type
Original Paper
Copyright
Copyright © 1959 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Landahl, H. D. Centroid orthogonal transformations. Psychometrika, 1938, 3, 219223.CrossRefGoogle Scholar
Reyburn, H. A. and Taylor, J. G.. Some factors of personality. Brit. J. Psychol., Gen. Sec., 1939, 30, 151165.Google Scholar
Swineford, F. A study in factor analysis: the nature of the general, verbal, and spatial bi-factors. Supplementary educ. Monogr., 1948, No. 67.Google Scholar
Thomson, G. H. The factorial analysis of human ability (3rd ed.), New York: Houghton Mifflin, 1948.Google Scholar