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The Theory about CD-CAT Based on FCA and Its Application

机译：基于FCA的CD-CAT理论及其应用

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Cognitive diagnosis (CD) plays an important role in intelligent tutoring system. Computerized adaptive testing (CAT) is adaptive, fair, and efficient, which is suitable to large-scale examination. Traditional cognitive diagnostic test needs quite large number of items, the efficient and tailored CAT could be a remedy for it, so the CAT with cognitive diagnosis (CD-CAT) is prospective. It is more benefit to the students who live in the developing area without rich source of teaching and distance education is adopted there. Although many researchers pay attention to CD, some flaws exist because it is still in its infancy (Leighton at el. 2007) and only a few researches of CD-CAT are gotten. In Tatsuoka's Q-matrix theory, it is wrong that the rows/columns could form a Boolean lattice. Based on Rule Space Model (RSM) and the Attribute Hierarchy Method (AHM), Formal Concept Analysis (FCA) is applied into CD-CAT. Concept lattices are served as the model of CD. The technology of item bank construction, item selection strategies in CD-CAT and estimation method are considered to design an initiatory and systemic CD-CA T which diagnoses examinees on-line and offers remedial measure for examinees in time. The algorithms of constructing concept lattice for CAT, diagnosing examinees and offering the best remedial measure to examinees are discussed theoretically in detail. The result of Monte Carlo study shows that examinees 'knowledge states are well diagnosed and the precision in examinees 'abilities estimation is satisfied.
机译：认知诊断（CD）在智能补习系统中扮演着重要角色。计算机自适应测试（CAT）具有自适应性，公平性和高效性，适用于大规模检查。传统的认知诊断测试需要大量的项目，有效且量身定制的CAT可能是一种补救方法，因此具有认知诊断的CAT（CD-CAT）是有前途的。对于生活在发展中地区但没有丰富的教学资源并且在那里采用远程教育的学生来说，这更有利。尽管许多研究人员关注CD，但由于CD仍处于起步阶段，因此存在一些缺陷（Leighton等，2007年），并且对CD-CAT的研究很少。在Tatsuoka的Q矩阵理论中，行/列可以形成布尔晶格是错误的。基于规则空间模型（RSM）和属性层次方法（AHM），将形式概念分析（FCA）应用于CD-CAT。概念格用作CD的模型。结合项目库建设技术，CD-CAT项目选择策略和估算方法，设计了一种系统的，可在线诊断应试者并及时为应试者提供补救措施的CD-CAT。从理论上详细讨论了构建CAT概念格，诊断应试者并为应试者提供最佳补救措施的算法。蒙特卡洛研究的结果表明，对应试者的知识状态进行了很好的诊断，并且满足了应试者能力估计的精度。

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