A Generalized Approach to Defining Item Discrimination for DCMs

Abstract

ABSTRACTDiagnostic classification models (DCMs, also known as cognitive diagnosis models) hold the promise of providing detailed classroom information about the skills a student has or has not mastered. Specifically, DCMs are special cases of constrained latent class models where classes are defined based on mastery/nonmastery of a set of attributes (or “facets”). In addition to identifying an examinee’s mastery profile, DCMs provide student information that can be used to describe the quality of an item, or the item discrimination. This paper discusses a unified item and test discrimination approach for identifying good and bad DCM items for polytomous models that is on an interpretable scale. Furthermore, this index is defined in a way such that for dichotomous DCMs, such as the DINA it reduces to traditional measures of item discrimination. Finally, using a simulation study, this index is shown to be related to both Kullback–Liebler-based indices and correct classification rates.