Generalized extreme value IRT models

This paper introduces two new Item Response Theory (IRT) models, based on the Generalized Extreme Value (GEV) distribution. These new models have asymmetric item characteristic curves (ICC) which have drawn growing interest, as they may better model actual item response behaviours in specific scenarios. The analysis of the models is carried out using a Bayesian approach, and their properties are examined and discussed. The validity of the models is verified by means of extensive simulation studies to evaluate the sensitivity of the model to the choice of priors on the new item parameter introduced, the accuracy of the parameters' recovery, as well as an assessment of the capacity of model comparison criteria to choose the best model against other IRT models. The new models are exemplified using real data from two mathematics tests, one applied in Peruvian public schools and another one administered to incoming university students in Chile. In both cases, the proposed models showed to be a promising alternative to asymmetric IRT models, offering new insights into item response modelling.