Cognitive Diagnostic Attribute-Level Discrimination Indices

Cognitive diagnostic models (CDMs) model the probability of correctly answering an item as a function of an examinee's attribute mastery pattern. Because estimation of the mastery pattern involves more than a continuous measure of ability, reliability concepts introduced by classical test theory and item response theory do not apply. The cognitive diagnostic index (CDI) measures an item's overall discrimination power, which indicates an item's usefulness in examinee attribute pattern estimation. Because of its relationship with correct classification rates, the CDI was shown to be instrumental in cognitively diagnostic test assembly. This article generalizes the CDI to attribute-level discrimination indices for an item. Two different attribute-level discrimination indices are defined; their relationship with correct classification rates is explored using Monte Carlo simulations. There are strong relationships between the defined attribute indices and correct classification rates. Thus, one important potential application of these indices is test assembly from a CDM-calibrated item bank.