属性多级化的认知诊断模型拓展及其Q矩阵设计

Extension of Cognitive Diagnosis Models Based on the Polytomous Attributes Framework and Their Q-matrices Designs

本研究在传统0-1属性的基础上,拓展出可以处理属性多级化的认知诊断模型——PA-rRUM和PA-DINA模型。Monte Carlo模拟研究表明:拓展模型具有较高的属性诊断正确率和参数估计精度,且参数估计的稳定性较强,说明拓展模型基本可行,可以用于实现多级化属性的认知诊断。这弥补了传统0-1化属性认知诊断模型的不足,具有较好的发展和应用前景;同时本研究还探讨了拓展模型性能及属性多级化下测验Q矩阵的设计。总之,本研究对于进一步拓展认知诊断在实践中的应用提供了重要的方法和技术支持。

Based on the traditional cognitive diagnosis models（CMDs）, this study developed two new cognitive diagnosis models, PA-rRUM and PA-DINA model respectively, to handle the polytomous attributes. Through Monte Carlo simulation, it indicated that： The parameters in the models could be identified, and robustness of the parameter estimation is relatively strong. Furthermore, the correct match ratios and accuracies of parameter estimation are decent. All these findings verified that the models are feasible for ploytomous attribute cognitive diagnosis. It also found that the precision of might be influenced by the sample size and the number of replications for the R＊P matrix. The larger the sample size is, or the greater the number of replications is, the more precise they might be. The results suggested that the Q matrix should include the R＊P matrix while the attribute is polytomous. In conclusion, the models overcame the shortcomings stemmed from dichotomous attribute models, thus they might provide a richer diagnostic result and more flexible models.