Item Response Theory (IRT) models the interaction between latent traits and responses in psychological assessments. My latest article introduces a new approach by incorporating group-theoretic symmetry constraints to improve IRT parameter estimation. By formalizing algebraic structures with group actions on item parameters like difficulty and discrimination, this method captures regularities within test items that are often overlooked by traditional estimation techniques.
Specifically, group actions on item parameters, such as difficulty, are represented through permutation matrices. This process reduces the dimensionality of the parameter space by collapsing symmetrically related items into equivalence classes, resulting in more efficient and theoretically consistent parameter estimates. The model also introduces dynamic, data-driven bounds for discrimination parameters, ensuring they reflect real variability without losing theoretical integrity.
While this method primarily focuses on the two-parameter logistic (2PL) model, it can be adapted to more complex models, such as the three- and four-parameter models (3PL and 4PL). Future developments aim to validate its empirical effectiveness and scalability across diverse psychometric scenarios.
Read the article here: https://www.cogn-iq.org/doi/10.2024/34d128d888faa98f72aa
