New Paradigm of Identifiable General-response Cognitive Diagnostic Models: Beyond Categorical Data.

IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Psychometrika Pub Date : 2024-07-05 DOI:10.1007/s11336-024-09983-4
Seunghyun Lee, Yuqi Gu
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Abstract

Cognitive diagnostic models (CDMs) are a popular family of discrete latent variable models that model students' mastery or deficiency of multiple fine-grained skills. CDMs have been most widely used to model categorical item response data such as binary or polytomous responses. With advances in technology and the emergence of varying test formats in modern educational assessments, new response types, including continuous responses such as response times, and count-valued responses from tests with repetitive tasks or eye-tracking sensors, have also become available. Variants of CDMs have been proposed recently for modeling such responses. However, whether these extended CDMs are identifiable and estimable is entirely unknown. We propose a very general cognitive diagnostic modeling framework for arbitrary types of multivariate responses with minimal assumptions, and establish identifiability in this general setting. Surprisingly, we prove that our general-response CDMs are identifiable under Q -matrix-based conditions similar to those for traditional categorical-response CDMs. Our conclusions set up a new paradigm of identifiable general-response CDMs. We propose an EM algorithm to efficiently estimate a broad class of exponential family-based general-response CDMs. We conduct simulation studies under various response types. The simulation results not only corroborate our identifiability theory, but also demonstrate the superior empirical performance of our estimation algorithms. We illustrate our methodology by applying it to a TIMSS 2019 response time dataset.

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可识别的一般反应认知诊断模型新范例:超越分类数据
认知诊断模型(CDM)是一种流行的离散潜变量模型,用于模拟学生掌握或缺乏多种精细技能的情况。认知诊断模型最广泛地应用于对二元或多态响应等分类项目响应数据建模。随着技术的进步和现代教育评估中不同测试形式的出现,新的反应类型也已出现,包括连续反应(如反应时间)和来自重复任务或眼动传感器测试的计数值反应。最近有人提出了 CDM 的变体,用于对这些反应建模。然而,这些扩展的 CDM 是否可以识别和估算还完全未知。我们为任意类型的多变量反应提出了一个非常通用的认知诊断建模框架,假设条件极少,并在这一通用环境中建立了可识别性。令人惊讶的是,我们证明了我们的一般反应 CDM 在基于 Q 矩阵的条件下是可识别的,这与传统分类反应 CDM 的条件相似。我们的结论为可识别的一般响应 CDM 树立了一个新范例。我们提出了一种 EM 算法,用于有效估计一大类基于指数族的一般响应 CDM。我们对各种反应类型进行了模拟研究。模拟结果不仅证实了我们的可识别性理论,还证明了我们的估计算法具有卓越的经验性能。我们将我们的方法应用于 TIMSS 2019 反应时间数据集,以说明我们的方法。
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来源期刊
Psychometrika
Psychometrika 数学-数学跨学科应用
CiteScore
4.40
自引率
10.00%
发文量
72
审稿时长
>12 weeks
期刊介绍: The journal Psychometrika is devoted to the advancement of theory and methodology for behavioral data in psychology, education and the social and behavioral sciences generally. Its coverage is offered in two sections: Theory and Methods (T& M), and Application Reviews and Case Studies (ARCS). T&M articles present original research and reviews on the development of quantitative models, statistical methods, and mathematical techniques for evaluating data from psychology, the social and behavioral sciences and related fields. Application Reviews can be integrative, drawing together disparate methodologies for applications, or comparative and evaluative, discussing advantages and disadvantages of one or more methodologies in applications. Case Studies highlight methodology that deepens understanding of substantive phenomena through more informative data analysis, or more elegant data description.
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