Abstract

In 2010, the Samejima-Bolfarine-Bazan (SBB) Item Response Theory (IRT) models were introduced by (Journal of Educational and Be-havioral Statistics 35 (2010) 693-713) under a Bayesian approach. These models extend the regular Bayesian One and Two Parameter Logistic IRT models by incorporating a parameter accounting for asymmetry of the Item Characteristic Curve (ICC) which is named the complexity of the item. It includes the Logistic Positive Exponent (LPE) IRT model formulated ini-tially by (Psychometrika 65 (2000) 319-335) and the Reflection of the LPE (RLPE). In the present work, new properties of the SBB models are devel-oped including a random effect for testlet structures with a Bayesian inference through a Markov chain Monte Carlo (MCMC) algorithm which includes the parameter estimation and model comparison. The asymmetric behavior of the Item Characteristic Curve (ICC) is detected using a marginal item informa-tion function. Two simulation studies are developed to analyze the sensitive-ness of the penalized parameter in the asymmetric behavior of the ICC and to evaluate the parameter recovery of the proposed model. A real data set, with a testlet structure and empirical evidence of asymmetric behavior of the ICCs, is used to apply the models.