An Illustration of the Two-Tier Item Factor Analysis Model

Authored by: Wes E. Bonifay

Handbook of Item Response Theory Modeling

Print publication date:  December  2014
Online publication date:  November  2014

Print ISBN: 9781848729728
eBook ISBN: 9781315736013
Adobe ISBN: 9781317565703


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Multidimensional item response theory (IRT) presumes that the items on a test measure multiple underlying latent constructs. Thanks to the introduction of item factor analysis (IFA; Bock, Gibbons, & Muraki, 1988) and recent advances in efficient estimation of complex latent variable models (e.g., Rijmen, Vansteelandt, & De Boeck, 2008), multidimensional IRT has become increasingly popular in the modeling of item responses. Specifically, the standard (correlated-traits) multidimensional IRT model (see Reckase, 2009) and more sophisticated models such as the item bifactor model (Gibbons & Hedeker, 1992) and the testlet response model (Bradlow, Wainer, & Wang, 1999) have seen widespread use in psychological and educational measurement.

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