Revisiting the Samejima–Bolfarine–Bazán IRT models: New features and extensions

Abstract

In 2010, the Samejima–Bolfarine–Bazán (SBB) Item Response Theory (IRT) models were introduced by (Journal of Educational and Behavioral 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 initially by (Psychometrika 65 (2000) 319–335) and the Reflection of the LPE (RLPE). In the present work, new properties of the SBB models are developed 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 information function. Two simulation studies are developed to analyze the sensitiveness 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.