The Effects of Incomplete Q-Matrix on Parameter Estimates and Classification Accuracy in the DINA and DINO Models and Non-parametric Approach

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There has been growing interest in Q-matrix based cognitive diagnosis models to assess examinees’ attribute profiles. The completeness of Q-matrix is important for assuring the identification of all attribute profile classes. However, it is often difficult to have assessments with complete Q-matrix especially when the number of attributes of interest is large. The main objective of this research it to study the effects of incomplete Q-matrix on the classification accuracy of examinees’ attribute profiles and on the parameter estimates for the cognitive diagnosis models. We investigate the effects of incomplete Q-matrix in the DINA/DINO models and the non-parametric method suggested by Chiu& Douglas (2013). Simulation studies are carried out to study the effects of incomplete Q-matrix under different scenarios. The idea of the equivalence class is used on the classification accuracy for these three models to explore the effect of incomplete Q-matrix. Our results show that the effects of incomplete Q-matrix were not as formidable as we expected, especially for the cases where the imprecise classification will happen even with complete Q-matrix. As for the classification accuracy, the parametric model is more robust than the non-parametric approach. Moreover, incomplete Q-matrix did not have a significant effect on the maximum likelihood estimation of item parameters.



認知診斷, 不完備的Q矩陣, DINA, DINO, 無母數方法, 等價分類, Cognitive Diagnosis, Incomplete Q-matrix, DINA, DINO, Non-parametric Classification, Equivalence Class