Location Indices for Ordinal Polytomous Items Based on Item Response Theory

Abstract

Polytomous items are typically described by multiple category‐related parameters; situations, however, arise in which a single index is needed to describe an item's location along a latent trait continuum. Situations in which a single index would be needed include item selection in computerized adaptive testing or test assembly. Therefore single location indices for ordinal polytomous items are proposed and studied. The proposed location indices (LIs) for polytomous items are mathematically derived based on the item category response functions (ICRFs) and item response function (IRF) for polytomous items. The ICRF approach resulted in three indices: LImean, LItrimmed mean, and LImedian, and the IRF approach resulted in one proposed index, LIIRF. An empirical example of real items is presented to help comprehension of the new location indices. Possible testing applications where the proposed item location indices are useful are discussed.