Hostname: page-component-7dd5485656-6kn8j Total loading time: 0 Render date: 2025-10-30T06:58:39.417Z Has data issue: false hasContentIssue false
  • English
  • Français

Exploratory Bi-Factor Analysis

Published online by Cambridge University Press:  01 January 2025

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

Abstract

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger. The bi-factor model has a general factor and a number of group factors. The purpose of this article is to introduce an exploratory form of bi-factor analysis. An advantage of using exploratory bi-factor analysis is that one need not provide a specific bi-factor model a priori. The result of an exploratory bi-factor analysis, however, can be used as an aid in defining a specific bi-factor model. Our exploratory bi-factor analysis is simply exploratory factor analysis using a bi-factor rotation criterion. This is a criterion designed to approximate perfect cluster structure in all but the first column of a rotated loading matrix. Examples are given to show how exploratory bi-factor analysis can be used with ideal and real data. The relation of exploratory bi-factor analysis to the Schmid–Leiman method is discussed.

Keywords

bi-factor rotationgeneral factorgroup factorgradient projection algorithmsHolzinger’s bi-factor methodSchmid–Leiman method

Information

Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 4 , October 2011 , pp. 537 - 549
Copyright
Copyright © 2011 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

An erratum to this article is available at http://dx.doi.org/10.1007/s11336-013-9346-0.

References

Bernaards, C.A., Jennrich, R.I. (2003). Orthomax rotation and perfect simple structure. Psychometrika, 68, 585–588.CrossRefGoogle Scholar
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, 189–225.CrossRefGoogle Scholar
Harman, H.H. (1976). Modern factor analysis, (3rd ed.). Chicago: The University of Chicago Press.Google Scholar
Holzinger, K.J., Swineford, S. (1937). The Bi-factor method. Psychometrika, 47, 41–54.CrossRefGoogle Scholar
Jennrich, R.I. (2001). A simple general procedure for orthogonal rotation. Psychometrika, 66, 289–306.CrossRefGoogle Scholar
Patrick, C.J., Hicks, B.M., Nichol, P.E., Krueger, R.F. (2007). A bi-factor approach to modeling the structure of the Psychopathy checklist-revisited. Journal of Personality Disorders, 21, 118–141.CrossRefGoogle Scholar
Pomplun, M. (2007). A bifactor analysis for a mode-of-administration effect. Applied Measurement in Education, 20, 137–152.CrossRefGoogle Scholar
Reise, S.P., Morizot, J., Hays, R.D. (2007). The role of the bifactor model in resolving dimensionality issues in health outcomes measures. Medical Care, 16, 19–31.Google ScholarPubMed
Reise, S.P., Moore, T.M., Haviland, M.G. (2010). Bi-factor models and rotations: Exploring the extent to which multidimensional data yield univocal scale scores. Journal of Personality Assessment, 92, 544–559.CrossRefGoogle Scholar
Schmid, J., Leiman, J.M. (1957). The development of hierarchical factor solutions. Psychometrika, 22, 53–61.CrossRefGoogle Scholar
Simms, L.J., Grös, D.F., Watson, D., O’Hara, M.W. (2008). Parsing the general and specific components of depression and anxiety with bifactor modeling. Depression and Anxiety, 25, E34–E46.CrossRefGoogle ScholarPubMed
Yung, Y.-F., Thissen, D., McLeod, L.D. (1999). On the relation between the higher-order factor model and the hierarchical factor model. Psychometrika, 64, 113–128.CrossRefGoogle Scholar