多値アトリビュートにおける認知診断の正確度へのQ行列の誤設定の影響

—アトリビュートの階層性がある場合の検討—

抄録

Cognitive diagnostic models (CDMs) are a class of statistical models that diagnose the mastery of respondents' cognitive traits, which are called attributes or skills. In the typical applications of CDMs, the Q-matrix, which represents which attributes are measured by each item, is specified by domain experts. In the case of dichotomous attributes, the impacts of Q-matrix misspecification on the classification accuracy have recently been studied; however, the case of polytomous attributes has not been reported. Therefore, in the present study, we examined how the difference between true and misspecified Q-matrix elements affects classification accuracy under four forms of attribute hierarchies. It was revealed that, in most conditions, larger difference between true and misspecified values resulted in lower classification accuracy. The impact of misspecification was the largest under the linear form of attribute hierarchy, which could be due to its smaller number of items that measure attribute levels. These results suggest that the number of items assigned to each attribute levels can be a key factor that affects the classification accuracy, especially when the degree of misspecification is large.