Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-08T12:15:15.327Z Has data issue: false hasContentIssue false
  • English
  • Français

Best Univocal Estimates of Orthogonal Common Factors

Published online by Cambridge University Press:  01 January 2025

A. Ralph Hakstian ,
James V. Zidek  and
Roderick P. McDonald
A. Ralph Hakstian*
Affiliation:
University of British Columbia
James V. Zidek
Affiliation:
University of British Columbia
Roderick P. McDonald
Affiliation:
The Ontario Institute for Studies in Education
*
Requests for reprints should be sent to A. Ralph Hakstian, Department of Psychology, University of British Columbia, Vancouver, British Columbia, CANADA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A general formulation is presented for obtaining conditionally unbiased, univocal common-factor score estimates that have maximum validity for the true orthogonal factor scores. We note that although this expression is formally different from both Bartlett's formulation and Heermann's approximate expression, all three, while developed from very different rationales, yield identical results given that the common-factor model holds for the data. Although the true factor score validities can be raised by a different non-orthogonal transformation of orthogonalized regression estimates—as described by Mulaik—the resulting estimates lose their univocality.

Keywords

factor scorescommon-factor analysisunivocal factor score estimates
Type
Notes And Comments
Information
Psychometrika , Volume 42 , Issue 4 , December 1977 , pp. 627 - 630
Copyright
Copyright © 1977 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

Bartlett, M. S. The statistical conception of mental factors. British Journal of Psychology, 1937, 28, 97–104.Google Scholar
Browne, M. W. On oblique Procrustes rotation. Psychometrika, 1967, 32, 125–132.CrossRefGoogle ScholarPubMed
Guilford, J. P., & Michael, W. B. Approaches to univocal factor scores. Psychometrika, 1948, 13, 1–22.CrossRefGoogle ScholarPubMed
Harris, C. W. On factors and factor scores. Psychometrika, 1967, 32, 363–379.CrossRefGoogle Scholar
Heermann, E. F. Univocal or orthogonal estimators of orthogonal factors. Psychometrika, 1963, 28, 161–172.CrossRefGoogle Scholar
Horst, P. Factor analysis of data matrices, 1965, New York: Holt, Rinehart & Winston.Google Scholar
Ledermann, W. On a shortened method of estimation of mental factors by regression. Psychometrika, 1939, 4, 109–116.CrossRefGoogle Scholar
McDonald, R. P., & Burr, E. J. A comparison of four methods of constructing factor scores. Psychometrika, 1967, 32, 381–401.CrossRefGoogle Scholar
Mosier, C. I. Determining a simple structure when loadings for certain tests are known. Psychometrika, 1939, 4, 149–162.CrossRefGoogle Scholar
Mulaik, S. A. The foundations of factor analysis, 1972, New York: McGraw-Hill.Google Scholar