A Simple And Efficient Method In Cognitive Diagnose Assessment—Hamming Distance Discrimination

Cognitive Diagnosis Assessment(CDA) employed psychometric model which is embedded in cognitive variables to diagnostic and assess subjects’ knowledge structure, processing skill, or cognitive process. Compare with the Classical Testing Theory(CTT) and Item Response Theory(IRT), the CDA can provide more complete and diagnosis information in detail.CDA relies on psychometric model which is based on complicated statistics and psychometric knowledge. These are so-called parameterized CDA methods. They request a lot of knowledge about probability and statistics, higher mathematics, linear algebra and calculus. It is difficult for researchers to apply these methods to explain the diagnostic result, not to mention the practitioner who is lack of these knowledge. Besides, the parameterized CDA methods depend on precise parameter estimation method, the estimation method itself has some deficiency. For example, the EM algorithm always convergent to locally-optimal extrema, and the MCMC consume excessive CPU time, and even unable to judge whether it has convergent to the truth. Therefore, these problems limit the CDA’s application and extension.Nonparametric CDA method only need Q matrix and response matrix to perform classification. It’s simplicity and conveniency makes it suitable to the real test condition. This article introduces a new approach called Hamming Distance Discrimination(HDD) which is based on the Q-matrix theory. According to the discrimination, two solutions based on HD are proposed: the random method(Method R) and the Bayesian method(Method B). In the Monte Carlo simulation study, the pattern match ratio and average attribute match ratio were used as criteria to evaluate the classification accuracy of DINA, Generalized Distance Discrimination(GDD), weighted Hamming distance(WH) and HDD. The result shows HDD is more convenient and is of high classification accuracy. The main conclusions as follow:(1)Attribute hierarchy has an effect on the classification accuracy of the five CDA methods.(2)Classification accuracy rate from high to low respectively: B method of HDD, DINA model, HDD R method, WH and GDD. The HDD B method and DINA models have same high classification accuracy.(3)The total number of items is proportional to the cognitive diagnosis method of classification accuracy(4)Sample size smaller has influence on cognitive diagnosis method of classification accuracy(5)Number of attributes is inversely proportional to the cognitive diagnosis method of classification accuracy(6)Classification accuracy rate from high to low respectively: negative skewness distribution, normal distribution, uniform distribution, positive skewness distribution...