Regularized Variational Estimation for Exploratory Item Factor Analysis

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Multidimensional Item Response Theory (MIRT) models the relationship between latent traits and item responses.
• Accurate specification of item factor loading structure is critical for MIRT's validity.
• Existing methods may struggle with high-dimensional data and accurate structure recovery.

Purpose of the Study:

• To propose a novel regularized Gaussian Variational Expectation Maximization (GVEM) algorithm for inferring item factor loading structure in MIRT.
• To develop a computationally efficient method suitable for high-dimensional MIRT applications.
• To accurately recover the item factor loading structure directly from data.

Main Methods:

• Developed a regularized GVEM algorithm incorporating an L1-type penalty.
• The penalty shrinks certain item factor loadings to zero, aiding structure identification.
• Algorithm leverages computational efficiency of GVEM for high-dimensional MIRT.

Main Results:

• Simulation studies demonstrate accurate recovery of the loading structure.
• The proposed method shows significant computational efficiency.
• The algorithm's effectiveness is illustrated with real-world educational assessment data (NELS:88).

Conclusions:

• The regularized GVEM algorithm provides an efficient and accurate approach for inferring MIRT item factor loading structures.
• This method is well-suited for complex, high-dimensional psychometric and educational measurement applications.
• The findings contribute to improved item parameter calibration and latent trait estimation in MIRT.