The Potential for Interpretational Confounding in Cognitive Diagnosis Models

Binary examinee mastery/nonmastery classifications in cognitive diagnosis models may often be an approximation to proficiencies that are better regarded as continuous. Such misspecification can lead to inconsistencies in the operational definition of "mastery" when binary skills models are assumed. In this paper we demonstrate the potential for an interpretational confounding of the latent skills when truly continuous skills are treated as binary. Using the DINA model as an example, we show how such forms of confounding can be observed through item and/or examinee parameter change when (1) different collections of items (such as representing different test forms) previously calibrated separately are subsequently calibrated together; and (2) when structural restrictions are placed on the relationships among skill attributes (such as the assumption of strictly nonnegative growth over time), among other possibilities. We examine these occurrences in both simulation and real data studies. It is suggested that researchers should regularly attend to the potential for interpretational confounding by studying differences in attribute mastery proportions and/or changes in item parameter (e.g., slip and guess) estimates attributable to skill continuity when the same samples of examinees are administered different test forms, or the same test forms are involved in different calibrations.