Chiu Chia-Yi, Köhn Hans-Friedrich
Rutgers, The State University of New Jersey, New Brunswick, New Jersey, USA.
University of Illinois at Urbana-Champaign, Champaign, Illinois, USA.
Br J Math Stat Psychol. 2015 Nov;68(3):387-409. doi: 10.1111/bmsp.12055. Epub 2015 Apr 15.
The Asymptotic Classification Theory of Cognitive Diagnosis (Chiu et al., 2009, Psychometrika, 74, 633-665) determined the conditions that cognitive diagnosis models must satisfy so that the correct assignment of examinees to proficiency classes is guaranteed when non-parametric classification methods are used. These conditions have only been proven for the Deterministic Input Noisy Output AND gate model. For other cognitive diagnosis models, no theoretical legitimization exists for using non-parametric classification techniques for assigning examinees to proficiency classes. The specific statistical properties of different cognitive diagnosis models require tailored proofs of the conditions of the Asymptotic Classification Theory of Cognitive Diagnosis for each individual model – a tedious undertaking in light of the numerous models presented in the literature. In this paper a different way is presented to address this task. The unified mathematical framework of general cognitive diagnosis models is used as a theoretical basis for a general proof that under mild regularity conditions any cognitive diagnosis model is covered by the Asymptotic Classification Theory of Cognitive Diagnosis.
认知诊断的渐近分类理论（Chiu等人，2009年，《心理测量学》，74卷，633 - 665页）确定了认知诊断模型必须满足的条件，以便在使用非参数分类方法时保证将考生正确分配到熟练程度等级。这些条件仅针对确定性输入噪声输出与门模型得到了证明。对于其他认知诊断模型，不存在使用非参数分类技术将考生分配到熟练程度等级的理论依据。不同认知诊断模型的具体统计特性需要针对每个模型分别证明认知诊断渐近分类理论的条件——鉴于文献中呈现的众多模型，这是一项繁琐的工作。本文提出了一种不同的方法来解决此任务。通用认知诊断模型的统一数学框架被用作一个通用证明的理论基础，该证明表明在适度的正则性条件下，任何认知诊断模型都涵盖在认知诊断渐近分类理论之中。
