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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant unlimited access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Bernaards, C.A., & Jennrich, R.I. (2003). Orthomax rotation and perfect simple structure. Psychometrika, 68, 585–588.
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.
Harman, H.H. (1976). Modern factor analysis (3rd ed.). Chicago: The University of Chicago Press.
Holzinger, K.J., & Swineford, S. (1937). The Bi-factor method. Psychometrika, 47, 41–54.
Jennrich, R.I. (2001). A simple general procedure for orthogonal rotation. Psychometrika, 66, 289–306.
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.
Pomplun, M. (2007). A bifactor analysis for a mode-of-administration effect. Applied Measurement in Education, 20, 137–152.
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.
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.
Schmid, J., & Leiman, J.M. (1957). The development of hierarchical factor solutions. Psychometrika, 22, 53–61.
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.
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.
An erratum to this article is available at http://dx.doi.org/10.1007/s11336-013-9346-0.
About this article
Cite this article
Jennrich, R.I., Bentler, P.M. Exploratory Bi-Factor Analysis. Psychometrika 76, 537–549 (2011) doi:10.1007/s11336-011-9218-4
- bi-factor rotation
- general factor
- group factor
- gradient projection algorithms
- Holzinger’s bi-factor method
- Schmid–Leiman method