贝叶斯模型是对小样本中 (a) 对称的项目响应模型的平均值
Fabio Setti1, Leah Feuerstahler1
1Department of Psychology, Fordham University, New York, New York, USA.
The British journal of mathematical and statistical psychology
|December 17, 2025
概括
贝叶斯模型平均 (BMA) 为小样本的项目响应理论 (IRT) 分析提供了一个实用的解决方案. 这种方法有效地探索项目不对称性,并在数据有限时估计项目响应函数 (IRF).
科学领域:
- 心理测量 心理测量 心理测量
- 统计建模 统计建模
- 教育测量教育的测量
背景情况:
- 非对称物件响应理论 (IRT) 模型提供了理论上的优势,但通常需要大样本大小才能可靠地估计参数.
- 传统的IRT模型在小样本中难以稳定,原因是估计众多项目参数的复杂性.
- 较新的非对称IRT模型,如负日志日志和补充日志日志,在项目响应函数 (IRF) 形状中提供灵活性,可以应用于较小的数据集.
研究的目的:
- 引入贝叶斯模型平均 (BMA) 作为探索项目不对称性和在小样本中估计IRF的方法.
- 与传统的模型选择和光滑技术相比,评估BMA对项目响应理论 (IRT) 分析的性能.
- 证明BMA在心理测量分析的项目和测试层面的可行性和有效性.
主要方法:
- 贝叶斯模型平均 (BMA) 应用于简单的对称和不对称物件响应理论 (IRT) 模型的组合.
- 拟议的BMA方法在经验数据集上进行了测试,以证明可行性.
- 在各种复杂的数据生成条件下,使用小样本大小 (N=100和N=250) 进行了模拟研究.
主要成果:
- 贝叶斯模型平均化 (BMA) 方法成功地确定了数据生成模型中存在的不对称性.
- 在模拟条件下,BMA方法在准确性方面始终超过了传统的模型选择和内核光滑技术.
- 经验示例证实了BMA在有限数据的项目响应理论 (IRT) 分析中的实际适用性.
结论:
- 贝叶斯模型平均 (BMA) 为小样本大小提供了复杂的非对称IRT模型的强大而实用的替代方案.
- 拟议的BMA方法为探索项目不对称性和估计心理测量研究中的项目响应函数 (IRF) 提供了一种灵活的方法.
- BMA是探索性的半参数物品响应理论 (IRT) 分析的宝贵工具,特别是在处理有限的数据时.
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