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

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• True score equating in item response theory (IRT) is complex for multidimensional IRT models due to the latent variable structure.
• The common-item nonequivalent groups design is frequently used in educational and psychological assessments.

Purpose of the Study:

• To introduce and evaluate two novel IRT true score equating procedures for bifactor models.
• To compare these new procedures against a standard unidimensional IRT model.

Main Methods:

• Developed an integration procedure by marginalizing specific factors in the bifactor model.
• Developed a PIRT-based procedure by projecting specific dimensions onto a general dimension, creating a locally dependent unidimensional IRT model.
• Compared equating results from both procedures with a unidimensional three-parameter logistic (3PL) model using simulated and real data.

Main Results:

• The integration and PIRT-based procedures yielded practically equivalent equating results.
• Both bifactor-based equating procedures demonstrated increased accuracy compared to the 3PL model as test multidimensionality increased.

Conclusions:

• The proposed integration and PIRT-based equating procedures are viable alternatives for bifactor models.
• These bifactor-based methods offer more accurate equating for tests with higher degrees of multidimensionality.