Inference of Correlations Among Testlet Effects: A Latent Variable Selection Method.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Testlet-based tests are popular in large-scale assessments.
• Standard bifactor models assume independent testlet effects, which is often unrealistic.
• Existing methods struggle to balance model interpretability with accounting for testlet correlations.

Purpose of the Study:

• To propose a data-driven method for learning significant correlations in the covariance matrix for testlet effects.
• To extend the bifactor model by incorporating these learned correlations.
• To maintain practical interpretability of sparse loading matrices.

Main Methods:

• A latent variable selection method is used for data-driven learning of correlations.
• Regularization is applied to weak correlations within an extended bifactor model.
• A stochastic expectation maximization algorithm is employed for computational efficiency.

Main Results:

• Simulation studies demonstrate the proposed method's consistency in identifying significant correlations.
• The method effectively models dependencies among testlets.
• Empirical analysis of 2015 Program for International Student Assessment data showcases practical application.

Conclusions:

• The proposed method offers a robust approach to modeling testlet effects in psychological and educational measurement.
• Accounting for testlet correlations improves the accuracy and interpretability of assessment models.
• This technique enhances the analysis of complex, large-scale assessment data.