基于类别水平的多级计分认知诊断Q矩阵修正：相对拟合统计量视角
摘要
<p id="C3">Cognitive diagnostic assessments (CDAs) can provide fine-grained diagnostic information about students' knowledge states, so as to help to teach in accordance with the students’ aptitude. The development of cognitive diagnosis model for polytomous response data expands the application scope of cognitive diagnostic assessment. As the basis of CDAs, Q-matrix has aroused more and more attention for the subjective tendency in Q-matrix construction that is typically performed by domain experts. Due to the subjective process of Q-matrix construction, there inevitably have some misspecifications in the Q-matrix, if left unchecked, can result in a serious negative impact on CDAs. To avoid the subjective tendency from experts and to improve the correctness of the Q-matrix, several objective Q-matrix validation methods have been proposed. Many Q-matrix validation methods have been proposed in dichotomous CDMs, however, the research of the Q-matrix validation method under polytomous CDMs is stalling lacking. To address this concern, several relative fit statistics (i.e., -2LL, AIC, BIC) were applied to the Q-matrix validation for polytomous cognitive diagnosis model in this research. The process of Q-matrix validation is as follows: <br/>First, the reduced Q-matrix is represented by${{Q}_{r}}$, which represents a set of potential q-vectors and contains ${{2}^{K}}-1$ possible q-vectors when attributes are independent. When validating the q-vector of the first category of item <italic>j</italic>, all possible q-vectors in${{Q}_{r}}$can be used as the q-vector of the first category of item <italic>j</italic>, and the Q-matrix of remaining items remains intact. From this, the item parameters and the attribute patterns of students can be estimated, and the -2LL, AIC, and BIC can be calculated accordingly. The q-vector with the largest likelihood (or smallest AIC/BIC) is regarded as the q-vector of the first category of item <italic>j</italic>. The q-vector of the next ca