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Full-Information Item Bi-Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Robert D. Gibbons  and
Donald R. Hedeker
Robert D. Gibbons*
Affiliation:
University of Illinois at Chicago
Donald R. Hedeker
Affiliation:
University of Illinois at Chicago
*
Requests for reprints should be sent to R. D. Gibbons, University of Illinois at Chicago, NPI 909A, 912 S. Wood, Chicago, IL 60612.
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Abstract

A plausible s-factor solution for many types of psychological and educational tests is one that exhibits a general factor and s − 1 group or method related factors. The bi-factor solution results from the constraint that each item has a nonzero loading on the primary dimension and at most one of the s − 1 group factors. This paper derives a bi-factor item-response model for binary response data. In marginal maximum likelihood estimation of item parameters, the bi-factor restriction leads to a major simplification of likelihood equations and (a) permits analysis of models with large numbers of group factors; (b) permits conditional dependence within identified subsets of items; and (c) provides more parsimonious factor solutions than an unrestricted full-information item factor analysis in some cases.

Keywords

bi-factor modelmarginal maximum likelihoodEM algorithmitem analysisdichotomous factor analysis
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 3 , September 1992 , pp. 423 - 436
Copyright
Copyright © 1992 The Psychometric Society

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Footnotes

Supported by the Cognitive Science Program, Office of Naval Research, Under grant #N00014-89-J-1104. We would like to thank Darrell Bock for several helpful suggestions.

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