Variational Bayesian inference for sparse item response theory models

Area of Science:

• Psychometrics
• Statistical Modeling
• Psychological Measurement

Background:

• Item response theory (IRT) is a statistical framework for analyzing the relationship between latent traits and observed responses.
• Factor loadings in IRT models can be sparse, posing challenges for accurate estimation.
• Existing IRT models may not adequately address the sparsity of factor loadings.

Purpose of the Study:

• To develop a novel sparse item response theory (IRT) model to handle sparse factor loadings.
• To introduce a variational Bayesian procedure for efficient posterior inference.
• To demonstrate the method's utility in psychological assessment.

Main Methods:

• A sparse IRT model is proposed with global and local shrinkage priors on factor loadings.
• A variational Bayesian inference procedure is developed.
• The logistic function is represented stochastically, framing the sparse IRT model as a mixture model with a Pólya-Gamma distribution for conjugate posterior computation.

Main Results:

• The proposed sparse IRT model effectively addresses factor loading sparsity.
• The variational Bayesian approach allows for straightforward posterior computation.
• Simulation studies confirm the performance of the new methodology.
• Application to personality assessment data illustrates practical utility.

Conclusions:

• The developed sparse IRT model offers an effective solution for analyzing sparse factor loadings.
• The variational Bayesian inference provides an efficient computational strategy.
• This methodology enhances the application of IRT in psychological trait assessment.