Modified Cognitive Diagnostic Index and Modified Attribute-Level Discrimination Index for Test Construction.

At present, there are only a limited number of studies examining how to optimally construct cognitive diagnostic tests. The cognitive diagnostic index (CDI) and attribute-level discrimination index (ADI) have been proposed to assemble such tests. The CDI and ADI have been shown to be instrumental in constructing cognitive diagnostic tests when the attribute relationships are assumed to be nonhierarchical. For greater generality when designing cognitive diagnostic assessment, attribute hierarchy and the ratio of test length to the number of attributes (RTA) are two important factors to be considered. This article proposes modified indices that take into account attribute hierarchy and RTA. Simulation studies show that, under the deterministic input, noisy, "and" gate model (DINA) and the reduced version of the reparameterized unified model (rRUM), the proposed indices provide higher attribute and attribute pattern correct classification rates than the original indices.