Approximating Bifactor IRT True-Score Equating With a Projective Item Response Model

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• True-score equating for bifactor models typically involves numerical integration to marginalize specific factors.
• An alternative approach uses projection to approximate numerical integration, offering potential advantages in parameter estimation.

Purpose of the Study:

• To compare the item response theory (IRT) true-score equating results obtained using projection versus numerical integration for bifactor models.
• To evaluate the feasibility of using projection with existing equating software that requires item parameters.

Main Methods:

• The study employed item response theory (IRT) and bifactor models.
• Numerical integration and a projection method were used to obtain marginalized bifactor models.
• Simulation studies were conducted to compare equating results from both methods.

Main Results:

• Simulation results indicated that projection and numerical integration produce highly comparable true-score equating outcomes.
• Projection provides item parameters for the marginalized bifactor model, facilitating use with standard equating software.

Conclusions:

• Projection serves as a viable and effective alternative to numerical integration for IRT true-score equating in bifactor models.
• The similarity in results suggests projection can be readily adopted, enhancing the practical application of equating methods.