Hostname: page-component-6898cfcb55-zsp5v Total loading time: 0 Render date: 2026-11-11T21:56:21.816Z Has data issue: false hasContentIssue false
  • English
  • Français

Exploratory Bi-factor Analysis: The Oblique Case

Published online by Cambridge University Press:  01 January 2025

Robert I. Jennrich and
Peter M. Bentler
Robert I. Jennrich*
Affiliation:
University of California, Los Angeles
Peter M. Bentler
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to Robert I. Jennrich, University of California, Los Angeles, 3400 Purdue Ave., Los Angeles, CA, USA. E-mail: rij@stat.ucla.edu
Get accessRights & Permissions [Opens in a new window]

Abstract

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford (Psychometrika 47:41–54, 1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler (Psychometrika 76:537–549, 2011) introduced an exploratory form of bi-factor analysis that does not require one to provide an explicit bi-factor structure a priori. They use exploratory factor analysis and a bifactor rotation criterion designed to produce a rotated loading matrix that has an approximate bi-factor structure. Among other things this can be used as an aid in finding an explicit bi-factor structure for use in a confirmatory bi-factor analysis. They considered only orthogonal rotation. The purpose of this paper is to consider oblique rotation and to compare it to orthogonal rotation. Because there are many more oblique rotations of an initial loading matrix than orthogonal rotations, one expects the oblique results to approximate a bi-factor structure better than orthogonal rotations and this is indeed the case. A surprising result arises when oblique bi-factor rotation methods are applied to ideal data.

Keywords

bi-factor rotationgeneral factorgroup factorgradient projection algorithmsoblique rotationorthogonal rotation

Information

Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 3 , July 2012, pp. 442 - 454
Copyright
Copyright © 2012 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

Footnotes

This research was supported by grants 5K05DA000017-33 and 5P01DA001070-37 from the National Institute on Drug Abuse to P.M. Bentler and grant 4R44CA137841-03 from the National Cancer Institute to P. Mair. Bentler acknowledges a financial interest in EQS and its distributor, Multivariate Software.

References

Browne, M.W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36, 111–150CrossRefGoogle Scholar
Cai, L., Yang, J.S., Hansen, M. (2011). Generalized full-information item bifactor analysis. Psychological Methods, 16, 221–248CrossRefGoogle ScholarPubMed
Chen, F.F., West, S.G., Sousa, K.H. (2006). A comparison of bifactor and second-order models of the quality of life. Multivariate Behavioral Research, 41, 189–225CrossRefGoogle Scholar
CONACE (2007). Descargar Septimo estudio nacional de drogas en poblacion escolar de Chile 2007. http://www.conace.cl/portal/index.php?option=com_content&view=article&id=280&Itemid=370. Google Scholar
Golay, P., Lecerf, T. (2011). On higher order structure and confirmatory factor analysis of the French Wechsler Adult Intelligence Scale (WAIS-III). Psychological Assessment, 23, 143–152CrossRefGoogle ScholarPubMed
Haviland, M.G., Warren, W.L., Riggs, M.L. (2000). An observer scale to measure alexithymia. Psychosomatics, 41, 385–392CrossRefGoogle ScholarPubMed
Holzinger, K.J., Swineford, S. (1937). The bi-factor method. Psychometrika, 47, 41–54CrossRefGoogle Scholar
Jennrich, R.I. (1973). Standard errors for obliquely rotated factor loadings. Psychometrika, 38, 593–604CrossRefGoogle Scholar
Jennrich, R.I. (2001). A simple general procedure for orthogonal rotation. Psychometrika, 66, 289–306CrossRefGoogle Scholar
Jennrich, R.I. (2002). A simple general method for oblique rotation. Psychometrika, 67, 7–20CrossRefGoogle Scholar
Jennrich, R.I., Bentler, P.M. (2011). Exploratory bi-factor analysis. Psychometrika, 76, 537–549CrossRefGoogle ScholarPubMed
Reise, S.P., Moore, T.M., Haviland, M.G. (2010). Bifactor models and rotations: exploring the extent to which multidimensional data yield univocal scores. Journal of Personality Assessment, 92, 544–559CrossRefGoogle ScholarPubMed
Schmid, J., Leiman, J.M. (1957). The development of hierarchical factor solutions. Psychometrika, 22, 53–61CrossRefGoogle Scholar
Yates, A. (1987). Multivariate exploratory data analysis: a perspective on exploratory factor analysis, Albany: State University of New York PressGoogle Scholar