Latent Variable Selection for Multidimensional Item Response Theory Models via [Formula: see text] Regularization.

Area of Science:

• Psychometrics
• Statistical Modeling
• Psychological Measurement

Background:

• Multidimensional item response theory (MIRT) models are complex, often requiring accurate identification of underlying latent traits.
• Selecting the correct latent structure is crucial for valid interpretation of MIRT results.
• Existing methods may struggle with identifying the precise number and nature of latent traits.

Purpose of the Study:

• To develop and validate a novel method for latent variable selection in MIRT.
• To accurately identify the latent traits measured by items in a multidimensional test.
• To provide an effective tool for researchers analyzing complex psychological data.

Main Methods:

• A penalized log-likelihood approach using an L1 penalty term is proposed.
• The Expectation-Maximization (EM) algorithm is combined with the coordinate descent algorithm for computation.
• The method's performance is evaluated through simulation studies.

Main Results:

• Simulation studies demonstrate the proposed estimator's effectiveness in correctly identifying latent structures.
• The method successfully identified relevant latent traits in a real-world dataset.
• The L1 penalty effectively aids in variable selection within the MIRT framework.

Conclusions:

• The developed latent variable selection method offers a robust approach for MIRT models.
• This technique enhances the interpretability and accuracy of latent trait identification.
• The application to the Eysenck Personality Questionnaire highlights its practical utility.