Generalized extreme value IRT models.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Traditional Item Response Theory (IRT) models often assume symmetry in item characteristic curves (ICC).
• Growing interest exists in asymmetric ICCs to better reflect real-world item response behaviors in specific contexts.
• The Generalized Extreme Value (GEV) distribution provides a flexible framework for developing such asymmetric models.

Purpose of the Study:

• Introduce two novel IRT models based on the GEV distribution, featuring asymmetric ICCs.
• Analyze the properties of these new models using a Bayesian approach.
• Evaluate the performance and applicability of the proposed asymmetric IRT models.

Main Methods:

• Development of two new IRT models incorporating the GEV distribution.
• Bayesian analysis to examine model properties and parameter estimation.
• Extensive simulation studies to assess prior sensitivity, parameter recovery, and model comparison.

Main Results:

• The proposed GEV-based IRT models successfully generate asymmetric ICCs.
• Simulation studies demonstrated the models' robustness to prior choices and accurate parameter recovery.
• Model comparison criteria effectively distinguished the new models from existing IRT alternatives.

Conclusions:

• The new GEV-based IRT models provide a valuable alternative for modeling asymmetric item response behaviors.
• Application to real data from Peruvian and Chilean mathematics tests confirmed their practical utility.
• These models offer new insights into item response modeling, particularly in educational assessment scenarios.