The Q-matrix identifies the subset of attributes measured by each item in the cognitive diagnosis modelling framework. Usually constructed by domain experts, the Q-matrix might contain some misspecifications, disrupting classification accuracy. Empirical Q-matrix validation methods such as the general discrimination index (GDI) and Wald have shown promising results in addressing this problem. However, a cut-off point is used in both methods, which might be suboptimal. To address this limitation, the Hull method is proposed and evaluated in the present study. This method aims to find the optimal balance between fit and parsimony, and it is flexible enough to be used either with a measure of item discrimination (the proportion of variance accounted for, PVAF) or a coefficient of determination (pseudo-R²). Results from a simulation study showed that the Hull method consistently showed the best performance and shortest computation time, especially when used with the PVAF. The Wald method also performed very well overall, while the GDI method obtained poor results when the number of attributes was high. The absence of a cut-off point provides greater flexibility to the Hull method, and it places it as a comprehensive solution to the Q-matrix specification problem in applied settings. This proposal is illustrated using real data.

中文翻译：

---

平衡拟合和简约以改进 Q 矩阵验证

Q 矩阵标识了认知诊断建模框架中每个项目测量的属性子集。通常由领域专家构建，Q 矩阵可能包含一些错误规范，从而破坏分类准确性。经验 Q 矩阵验证方法，例如一般鉴别指数(GDI) 和 Wald，已在解决此问题方面显示出有希望的结果。但是，这两种方法都使用了一个截止点，这可能不是最理想的。为了解决这个限制，在本研究中提出并评估了赫尔方法。该方法旨在找到拟合和简约之间的最佳平衡，它足够灵活，既可以用于项目歧视的度量（方差所占的比例）, PVAF) 或决定系数（伪R ²）。模拟研究的结果表明，赫尔方法始终表现出最佳性能和最短计算时间，尤其是与 PVAF 一起使用时。Wald 方法在整体上也表现得很好，而 GDI 方法在属性数量较多时获得的结果较差。没有截止点为 Hull 方法提供了更大的灵活性，并将其作为应用设置中 Q 矩阵规范问题的综合解决方案。这个提议是用真实数据来说明的。