结合规范化和后勤回归模型,验证认知诊断模型的Q矩阵
Xiaojian Sun1,2,3, Tongxin Zhang4, Chang Nie4
1School of Mathematics and Statistics, Southwest University, Chongqing, China.
概括
这项研究引入了一种新的规范化方法,用于在认知诊断模型中验证Q矩阵,提高准确性和效率,特别是在有限的数据的情况下.
科学领域:
- 教育测量教育的测量
- 心理测量 心理测量 心理测量
- 数据科学数据科学数据科学
背景情况:
- Q矩阵对于认知诊断模型 (CDM) 至关重要,但通常依赖于主观的专家判断,冒着错误的风险.
- 现有的Q矩阵统计验证方法,如MLR-B和Hull,在时间或准确性方面存在局限.
- 错误指定的Q矩阵可能会对诊断评估的可靠性产生负面影响.
研究的目的:
- 开发和评估用于Q矩阵验证的新型统计方法.
- 提高认知诊断中的Q矩阵验证的准确性和效率.
- 为了解决现有的Q矩阵验证技术的局限性.
主要方法:
- 提出了一种新方法,将L1规范化与基于多重逻辑回归 (MLR-B) 的模型相结合.
- 对于MLR模型的日志概率,应用了一个L1惩罚术语来改进每个项目的属性选择.
- 一项模拟研究比较了规范化的MLR-B方法与传统的MLR-B和船体方法.
主要成果:
- 规范化的MLR-B方法表明Q矩阵恢复率 (QRR) 和真正阳性率 (TPR) 优越,特别是在小样本大小的情况下.
- 与现有方法相比,新方法实现了略高的真负率 (TNR).
- 计算效率得到了提高,正规化的方法比MLR-B需要更少的时间,并且与Hull方法相比的时间相比.
结论:
- 规范化的MLR-B方法为认知诊断中的Q矩阵验证提供了更准确,更有效的方法.
- 这种方法有效地解决了错误指定的Q矩阵的问题,提高了CDM的可靠性.
- 这些发现表明,在现实世界的评估应用中使用这种规范化的方法具有实际优势.
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