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At present, most existing cognitive diagnosis models (CDMs) are designed to either identify the presence and absence of skills or misconceptions, but not both. This article proposes a CDM that can be used to simultaneously identify what skills and misconceptions students possess. In addition, it proposes the use of the expectation-maximization algorithm to estimate the model parameters. A simulation study is conducted to evaluate the viability of the proposed model and algorithm. Real data are analyzed to demonstrate the applicability of the proposed model, and compare it with existing CDMs. Furthermore, a real data-based simulation study is conducted to determine how the correct classification rates in the context of the proposed model can be improved. Issues related to the proposed model and future research are discussed.

A Cognitive Diagnosis Model for Identifying Coexisting Skills and Misconceptions