Ordinal response variation of the polytomous Rasch model

Polytomous Rasch model (PRM) is a general probabilistic measurement model widely used in psychometrics, social science and educational measurement. It describes the probability of certain ordinal response of an object under test as a function of its ability, given, so called thresholds, characterizing the specific test item. The model was also adapted to business and industry applications. In contrast to the behavior of the median PRM outcome value, monotonically increasing as the ability increases, the ordinal variation behavior, as shown in the article, can be very diverse and it is rather determined by the mutual position of the threshold values of the model. The article studies ordinal variation of the response vs. ability for different thresholds locations arrangements and different amounts of ordered response categories. It is shown under what circumstances this function becomes multimodal. If several objects are involved in the test, attention is paid to the possibility of the total variation decomposition into intra and inter components. Considering the intra object variation helps to avoid overestimation of the real variation between the tested objects as it is demonstrated by illustrative example.