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

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Footnotes

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

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