Scalability coefficients for two-level polytomous item scores: An introduction and an application

First, we made an overview of nonparametric item response models and the corresponding scalability coefficients in Mokken scale analysis for single-level item scores and two-level dichotomous item scores. Second, we generalized these models and coefficients to two-level polytomous item scores. Third, we applied the new scalability coefficients to a real-data example, and compared the outcomes with results obtained using single-level reliability analysis and single-level Mokken scale analysis. Results suggest that coefficients from single-level analyses do not provide accurate information about scalability of two-level item scores.