Abstract

Some asymmetric Item Characteristic Curves (ICC)s have already been introduced in the IRT literature. These proposals include a new item parameter associated with the item complexity which explains the asymmetry in the ICC. Although the importance of proposing new models that have asymmetric ICC in IRT is already known, the relationship between these models and unbalanced binary responses in testing data in real applications has not been explored. In this work we propose new asymmetric IRT models that have an asymmetric ICC as their main feature. A special case of these models is the cloglog IRT model. Bayesian estimation of the proposed models is discussed and one application in educational data illustrates the benefits of the new ICC when we compare our IRT models with other IRT models proposed in the literature.