基于信号检测理论的新 Q 矩阵验证方法。

IF 1.5 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS British Journal of Mathematical & Statistical Psychology Pub Date : 2024-11-19 DOI:10.1111/bmsp.12371
Jia Li, Ping Chen
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引用次数: 0

摘要

Q 矩阵是认知诊断理论的重要组成部分,也是认知诊断研究和实际应用的重要基础。在实际应用中,Q 矩阵通常由领域专家开发,可能包含一些错误的规范,因此需要使用 Q 矩阵验证方法对其进行完善。本文基于信号检测理论,提出了一种新的 Q 矩阵验证方法(即 β $$ \beta $$ 方法),并进行了仿真研究,将新方法与现有方法进行比较。结果表明,当模型为 DINA(确定性输入、噪声 "和 "门)时,β $ $ \beta $ $ 方法在所有条件下都优于现有方法;在广义 DINA(G-DINA)模型下,当样本量较小、项目质量较高或 Q 矩阵错误率≥.4 时,该方法仍具有最高的验证率。最后,分析了 PISA 2000 阅读评估的子数据集,以评估 β $$ \beta $$ 方法的可靠性。
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A new Q-matrix validation method based on signal detection theory.

The Q-matrix is a crucial component of cognitive diagnostic theory and an important basis for the research and practical application of cognitive diagnosis. In practice, the Q-matrix is typically developed by domain experts and may contain some misspecifications, so it needs to be refined using Q-matrix validation methods. Based on signal detection theory, this paper puts forward a new Q-matrix validation method (i.e., β $$ \beta $$ method) and then conducts a simulation study to compare the new method with existing methods. The results show that when the model is DINA (deterministic inputs, noisy 'and' gate), the β $$ \beta $$ method outperforms the existing methods under all conditions; under the generalized DINA (G-DINA) model, the method still has the highest validation rate when the sample size is small, and the item quality is high or the rate of Q-matrix misspecification is ≥.4. Finally, a sub-dataset of the PISA 2000 reading assessment is analysed to evaluate the reliability of the β $$ \beta $$ method.

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来源期刊
CiteScore
5.00
自引率
3.80%
发文量
34
审稿时长
>12 weeks
期刊介绍: The British Journal of Mathematical and Statistical Psychology publishes articles relating to areas of psychology which have a greater mathematical or statistical aspect of their argument than is usually acceptable to other journals including: • mathematical psychology • statistics • psychometrics • decision making • psychophysics • classification • relevant areas of mathematics, computing and computer software These include articles that address substantitive psychological issues or that develop and extend techniques useful to psychologists. New models for psychological processes, new approaches to existing data, critiques of existing models and improved algorithms for estimating the parameters of a model are examples of articles which may be favoured.
期刊最新文献
A new Q-matrix validation method based on signal detection theory. Discriminability around polytomous knowledge structures and polytomous functions. Understanding linear interaction analysis with causal graphs. Identifiability analysis of the fixed-effects one-parameter logistic positive exponent model. Regularized Bayesian algorithms for Q-matrix inference based on saturated cognitive diagnosis modelling.
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