认知诊断评估中基于布尔矩阵分解的数据驱动q矩阵学习

IF 1.5 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS British Journal of Mathematical & Statistical Psychology Pub Date : 2022-05-16 DOI:10.1111/bmsp.12271
Jianhua Xiong, Zhaosheng Luo, Guanzhong Luo, Xiaofeng Yu
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引用次数: 1

摘要

属性和q矩阵是认知诊断评估的核心组成部分,通常由领域专家定义。然而,对于专家来说,手动指定属性和q矩阵是具有挑战性和耗时的。因此,迫切需要一种自动和智能的手段来解决这一问题。本文提出了一种从响应数据中学习q矩阵的数据驱动方法。通过构造统计指标和基于布尔矩阵分解的启发式算法,将响应矩阵分解为q矩阵与属性掌握模式的布尔积。利用在各种条件下产生的模拟数据对所提出方法的可行性进行了评估。最后给出了一个实际的数据示例,以证明该方法的有效性。
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Data-driven Q-matrix learning based on Boolean matrix factorization in cognitive diagnostic assessment

Attributes and the Q-matrix are the central components for cognitive diagnostic assessment, and are usually defined by domain experts. However, it is challenging and time consuming for experts to specify the attributes and Q-matrix manually. Thus, there is an urgent need for an automatic and intelligent means to address this concern. This paper presents a new data-driven approach for learning the Q-matrix from response data. By constructing a statistical index and a heuristic algorithm based on Boolean matrix factorization, the response matrix is decomposed into the Boolean product of the Q-matrix and the attribute mastery patterns. The feasibility of the proposed approach is evaluated using simulated data generated under various conditions. A real data example is also presented to demonstrate the usefulness of the proposed approach.

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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.
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