Item response theory is a widely used framework for the design, scoring, and scaling of measurement instruments. Item response models are typically used for dichotomously scored questions that have only two score points (e.g., multiple-choice items). However, given the increasing use of instruments that include questions with multiple response categories, such as surveys, questionnaires, and psychological scales, polytomous item response models are becoming more utilized in education and psychology. This study aims to demonstrate the application of explanatory item response theory (IRT) models to polytomous item responses in order to explain common variability in item clusters, person groups, and interactions between item clusters and person groups. Explanatory forms of several IRT models -- such as Partial Credit Model and Rating Scale Model -- are demonstrated and the estimation procedures of these models are explained. Findings of this study suggest that explanatory IRT models can be more parsimonious than traditional IRT models for polytomous data when items and persons share common characteristics. Explanatory forms of the polytomous IRT models can provide more information about response patterns in item responses by estimating fewer item parameters.