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Exploratory Bi-Factor Analysis

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.

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Author information

Correspondence to Robert I. Jennrich.

Additional information

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

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Jennrich, R.I., Bentler, P.M. Exploratory Bi-Factor Analysis. Psychometrika 76, 537–549 (2011) doi:10.1007/s11336-011-9218-4

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Keywords

  • bi-factor rotation
  • general factor
  • group factor
  • gradient projection algorithms
  • Holzinger’s bi-factor method
  • Schmid–Leiman method