The Relationship between Parameters from Two Polytomous Item Response Theory Models

RESPONSE THEORY MODELS Various polytomous IRT models parameterize the probability of response categories differently from each other. For example, the graded response model (GRM) (Samejima, 1969) is based on the cumulative log-odds principle, whereas the generalized partial credit model (GPCM) (Muraki, 1992) is based on the adjacent log-odds principle. It is widely known that these two polytomous IRT models do not produce directly comparable parameters (e.g., Ostini & Nering, 2005). However, to our knowledge, it has not been clearly pointed out that how discrimination parameters (a-parameters, hereafter) from these two polytomous IRT models are affected by the number of response categories. Thus, this study investigates the relationship between the a-parameters and the number of response categories for polytomous item response theory models, specifically for the GRM and GPCM. The relationships are first explored algebraically. More specifically, the cumulative category response functions of the investigated models are solved with respect to the a-parameter. Then, the algebraically derived relationships are empirically demonstrated with simulated data sets. Finally, practical importance of the findings is discussed. Method Algebraic Demonstrations The formulas for the a-parameters based on the cumulative category response functions were derived for the GRM and GPCM. The category response functions of Samejima’s