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

Kyung Yong Kim¹, Uk Hyun Cho¹

¹The University of North Carolina at Greensboro, USA.

Applied Psychological Measurement

|April 29, 2020

Summary

Item response theory (IRT) true-score equating for bifactor models can use projection as an approximation to numerical integration. Both methods yield very similar results for equating, offering flexibility in analysis.

Keywords:

MIRT bifactor model equating item response theory projective item response theory

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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.