An alternative attribute map for polytomous assessment structures

The present paper introduces an attribute map that offers an alternative approach to modeling polytomous item–response relationships. This new attribute map is based on the principle that each available attribute can independently enable an item to reach a specific observable response level. The paper rigorously defines this attribute map and establishes the corresponding item–response function. Using these two maps, a coherent attribute structure is constructed, leading to a competence-based polytomous assessment structure. Finally, a straightforward mathematical example is provided to illustrate the validity and practical applicability of this theoretical framework.