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Full-Information Item Bifactor Analysis of Graded Response Data

University of Illinois, Chicago

R. Darrell Bock

University of Illinois, Chicago

Donald Hedeker

University of Illinois, Chicago

David J. Weiss

University of Minnesota

Eisuke Segawa

University of Illinois, Chicago

Dulal K. Bhaumik

University of Illinois, Chicago

David J. Kupfer

Western Psychiatric Institute

Ellen Frank

Western Psychiatric Institute

Victoria J. Grochocinski

Western Psychiatric Institute

Angela Stover

Western Psychiatric Institute

A plausible factorial structure for many types of psychological and educational tests exhibits a general factor and one or more group or method factors. This structure can be represented by a bifactor model. The bifactor structure results from the constraint that each item has a nonzero loading on the primary dimension and, at most, one of the group factors. The authors develop estimation procedures for fitting the graded response model when the data follow the bifactor structure. Using maximum marginal likelihood estimation of item parameters, the bifactor restriction leads to a major simplification of the 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. Analysis of data obtained from 586 chronically mentally ill patients revealed a clear bifactor structure.

Key Words: bi-factor model • maximum marginal likelihood • EM algorithm • item analysis • ordinal data • factor analysis

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