项目参数恢复:对先前分配的敏感性
Christine E DeMars1, Paulius Satkus2
1James Madison University, Harrisonburg, VA, USA.
Educational and psychological measurement
|July 26, 2024
概括
对于项目响应理论模型,将贝叶斯先验应用于边际最大概率估计,可以改善参数估计,特别是在小样本大小的情况下. 对于 >= 500 的样本,对 c-参数的先验是有益的,而对于 100 的样本,a-和 c-参数都需要先验.
科学领域:
- 心理测量 心理测量 心理测量
- 统计建模 统计建模
- 教育测量的教育测量.
背景情况:
- 边际最大概率 (MML) 是项目响应理论 (IRT) 模型的常用估计方法.
- 贝叶斯先验经常被纳入三参数后勤 (3PL) 模型的MML估计,特别是小样本大小,以解决估计挑战.
- 关于为MML估计选择合适的先验的指导是有限的.
研究的目的:
- 调查使用MML的3PL IRT模型中先前分布对参数估计的影响.
- 在不同样本大小的不同参数 (a,b,c) 上确定先验的有效性.
- 为了评估先前模式和强度对参数估计偏差和根平均平方误差 (RMSE) 的影响.
主要方法:
- 用不同的样本大小 (≤1000) 进行模拟研究.
- 使用边际最大概率对3PL IRT模型的估计.
- 对项目参数 (a,b,c) 应用贝叶斯先验.
- 在不同的先前条件下分析参数偏差和RMSE.
主要成果:
- 没有先验,小样本大小 (≤1000) 往往导致极端和不可思议的参数估计.
- 对于500个或更多样本的c参数的先验改进了估计.
- 对于大小为100的样本,需要对a和c参数进行先验.
- 参数偏差受先前模式的影响,但不显著受到先前强度的影响 (除非极具信息性).
- 对于a-和b-参数的RMSE显示出对先前模式或强度的依赖性最小.
- 对于c参数的RMSE受到c的先前模式的影响.
结论:
- 贝叶斯先验对于3PL IRT模型的稳定MML估计至关重要,尤其是在有限的数据的情况下.
- 战略性应用先验,特别是关于c参数的先验,可以减轻估计问题.
- 选择先前模式对于减少c参数估计偏差很重要.
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