A Cognitive Diagnosis Method Based on Mahalanobis Distance

Cognitive diagnosis methods (CDMs) is very important for cognitive diagnosis, the primary purpose for CDMs is to classify examinees into mutually exclusive categories. Although there exist many CDMs, researchers propose many better new CDMs. Among them, the generalized distance discrimination (GDD) and the Hamming distance discrimination (HDD) receive more and more attention for their advantages of simple and easy to use, high classification accuracy, thus, Mahalanobis distance discrimination (MDD), a generalized CDM is introduced. GDD and HDD are its special cases. Mahalanobis distance (MD) is employed for MDD to calculate the distance between an examinee’s observed response pattern (ORP) and all kinds of ideal response pattern (IRP). The Shannon entropy is specified as covariance. According to the principle of minimum distance and designing test blueprint, IRP can be bijection mapped to the state of knowledge. Under dichotomous model, the pattern match ratio and average attribute match ratio are selected as the criteria for evaluating the classification accuracy. The Monte Carlo simulation study shows that the performance of MDD is better than GDD and HDD.