Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-14T14:23:17.700Z Has data issue: false hasContentIssue false
  • English
  • Français

Orthomax Rotation and Perfect Simple Structure

Published online by Cambridge University Press:  01 January 2025

Coen A. Bernaards and
Robert I. Jennrich
Coen A. Bernaards*
Affiliation:
Division of Cancer Prevention and Control Research, UCLA Jonsson Comprehensive Cancer CenterDepartment of Statistics, University of California, Los Angeles
Robert I. Jennrich
Affiliation:
Department of Statistics, University of California, Los Angeles
*
Requests for reprints should be sent to Coen A. Bernaards, AMC Cancer Research Cemea, 1600 Pierce Street, Denver, CO 80214. E-Mail: bernaardsc@amc.org
Get accessRights & Permissions [Opens in a new window]

Abstract

A loading matrix has perfect simple structure if each row has at most one nonzero element. It is shown that if there is an orthogonal rotation of an initial loading matrix that has perfect simple structure, then orthomax rotation with 0 ≤γ ≤ 1 of the initial loading matrix will produce the perfect simple structure. In particular, varimax and quartimax will produce rotations with perfect simple structure whenever they exist.

Keywords

factor analysisorthogonal rotationquartimaxvarimax

Information

Type
Theory And Methods
Information
Psychometrika , Volume 68 , Issue 4 , December 2003, pp. 585 - 588
Copyright
Copyright © 2003 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.)

Article purchase

Temporarily unavailable

References

Browne, M.W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36, 111–150.10.1207/S15327906MBR3601_05CrossRefGoogle Scholar
Carroll, J.B. (1953). An analytic solution for approximating simple structure in factor analysis. Psychometrika, 18, 23–38.10.1007/BF02289025CrossRefGoogle Scholar
Ferguson, G.A. (1954). The concept of parsimony in factor analysis. Psychometrika, 19, 281–290.CrossRefGoogle Scholar
Gorsuch, R.L. (1983). Factor analysis 2nd ed., Hillsdale, NJ: Lawrence Erlbaum & Associates.Google Scholar
Harman, H.H. (1960). Modern factor analysis. Chicago, IL: The University of Chicago Press.Google Scholar
Harman, H.H. (1976). Modern factor analysis 3rd ed., Chicago, IL: The University of Chicago Press.Google Scholar
Kaiser, H.F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200.10.1007/BF02289233CrossRefGoogle Scholar
Kaiser, H.F. (1974). An index of factorial simplicity. Psychometrika, 39, 31–36.10.1007/BF02291575CrossRefGoogle Scholar
Neuhaus, J.O., Wrigley, C. (1954). The quartimax method: An analytical approach to orthogonal simple structure. British Journal of Statistical Psychology, 7, 81–91.10.1111/j.2044-8317.1954.tb00147.xCrossRefGoogle Scholar