A note on weighted likelihood and Jeffreys modal estimation of proficiency levels in polytomous item response models

Warm (in Psychometrika, 54, 427-450, 1989) established the equivalence between the so-called Jeffreys modal and the weighted likelihood estimators of proficiency level with some dichotomous item response models. The purpose of this note is to extend this result to polytomous item response models. First, a general condition is derived to ensure the perfect equivalence between these two estimators. Second, it is shown that this condition is fulfilled by two broad classes of polytomous models including, among others, the partial credit, rating scale, graded response, and nominal response models.