ABSTRACT
This chapter focuses on item response models for polytomously scored items. It categorizes the polytomous IRT models into three groups based on their scale of measurement and whether they are in the Rasch family of models: polytomous Rasch models for ordinal items, polytomous non-Rasch models for ordinal items, and polytomous IRT models for nominal items. Unlike polytomous Rasch models, the generalized partial credit model and the graded response model (GRM) assume that items vary in terms of their discrimination levels in distinguishing examinees or respondents with low and high latent traits. The GRM models the probability of a given response category or higher by following the same order as the response options. The mirt function is also capable of estimating a hybrid model that combines certain characteristics of the rating scale model and the GRM into a single model. The mirt function is capable of estimating traditional IRT models as well as their specialized forms for polytomous items.
