Application of Dimension Reduction to CAT Item Selection Under the Bifactor Model

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Multidimensional computerized adaptive testing (MCAT) utilizes bifactor models for complex measurement structures.
• Traditional item selection methods face computational challenges in high-dimensional bifactor MCAT.

Purpose of the Study:

• To adapt and evaluate advanced item selection methods for bifactor MCAT.
• To assess the performance of dimension reduction techniques in improving computational efficiency and estimation precision.

Main Methods:

• Applied dimension reduction to four item selection methods: posterior-weighted Fisher D-optimality (PDO), posterior expected Kullback-Leibler information (PKL), continuous entropy (CE), and mutual information (MI).
• Compared these methods with Bayesian D-optimality (BDO) using estimation precision as the primary metric.
• Investigated the impact of bifactor patterns and test length on estimation accuracy.

Main Results:

• When estimating both general and group factors, BDO, PDO, CE, and MI demonstrated comparable and superior performance over PKL.
• For estimating the general factor with group factors as nuisance dimensions, MI and CE yielded the best results, followed by BDO, PDO, and PKL.

Conclusions:

• Dimension reduction is effective in making advanced item selection methods feasible for bifactor MCAT.
• The choice of item selection method depends on whether general/group factors are primary targets or nuisance variables.