Item Response Theory True Score Equating for the Bifactor Model Under the Common-Item Nonequivalent Groups Design

Applying item response theory (IRT) true score equating to multidimensional IRT models is not straightforward due to the one-to-many relationship between a true score and latent variables. Under the common-item nonequivalent groups design, the purpose of the current study was to introduce two IRT true score equating procedures that adopted different dimension reduction strategies for the bifactor model. The first procedure, which was referred to as the integration procedure, linked the latent variable scales for the bifactor model and integrated out the specific factors from the item response function of the bifactor model. Then, IRT true score equating was applied to the marginalized bifactor model. The second procedure, which was referred to as the PIRT-based procedure, projected the specific dimensions onto the general dimension to obtain a locally dependent unidimensional IRT (UIRT) model and linked the scales of the UIRT model, followed by the application of IRT true score equating to the locally dependent UIRT model. Equating results obtained with the two equating procedures along with those obtained with the unidimensional three-parameter logistic (3PL) model were compared using both simulated and real data. In general, the integration and PIRT-based procedures provided equating results that were not practically different. Furthermore, the equating results produced by the two bifactor-based procedures became more accurate than the results returned by the 3PL model as tests became more multidimensional.