Equivalence of weighted likelihood and Jeffreys modal estimation of proficiency under polytomous item response models

This talk focuses on two proficiency level estimators in item response theory (IRT) framework: the weighted likelihood estimator (WLE) and the Jeffreys modal estimator (JME), that is, the usual Bayes modal estimator with Jeffreys’ non-informative prior. With dichotomously scored items, the WLE and the JME are completely equivalent under the two-parameter logistic model, while remarkable relationships were established under the three-parameter logistic model. The purpose of this talk is to extend such comparison to polytomously scored items. It is shown that both WLE and JME are also equivalent for two broad classes of polytomous IRT models, including, among others, the (modified) graded response model, the (generalized) partial credit model, the rating scale model and the nominal response model. Parallelisms with dichotomously scored items are drawn. An example from a real data set is used to illustrate this finding.