The Bayesian estimators of polytomous item response theory models with approximated conditional likelihood and their mathematical optimalities

In this study, we derive the Bayesian estimators of polytomous item response theory (IRT) models with an approximated conditional likelihood function and consider their mathematical optimalities. First, we derive Bayesian estimators of the rating scale model (RSM) and related IRT models with a conditional type approximated likelihood function proposed by [10]. Then, we evaluate the admissibility and minimaxity of these estimators. We then show the range of the approximation by the conditional likelihood method using a simulation study. An application is also presented.