使用双变潜因子模型的分散计时数据的联合分析
Cornelis J Potgieter1,2, Akihito Kamata3, Yusuf Kara4
1Texas Christian University, Fort Worth, Texas, USA.
The British journal of mathematical and statistical psychology
|August 28, 2025
概括
这项研究引入了联合计数和时间数据的新统计模型,提高了测量的准确性和速度. 贝塔双项模型改善了复杂数据的适应性,并提供了可靠的标准误差估计.
科学领域:
- 心理测量
- 统计模型
- 数据分析
背景情况:
- 准确度和速度的准确测量在各种领域至关重要.
- 现有的模型可能无法完全捕捉联合计时数据的复杂性.
- 计数数据中的过度分散是常见的,需要专门的分布.
研究的目的:
- 开发和评估一个具有双因素潜伏特征结构的联合计数时间数据模型.
- 通过蒙特卡洛预期最大化 (MCEM) 实现使用时刻方法 (MOM) 和最大概率估计 (MLE) 的参数估计.
- 评估标准错误估计方法的性能,特别是引导重新抽样.
主要方法:
- 对于计数变量使用Beta双项分布,对于时间变量使用日志常态分布.
- 用于时刻方法 (MOM) 估计器的衍生边际时刻.
- 使用蒙特卡罗预期最大化 (MCEM) 进行最大概率估计 (MLE).
- 使用观察到的信息矩阵和重新抽样的估计标准误差.
主要成果:
- 模拟研究证明了拟议的估计器的准确性和计算效率.
- 引导重新抽样显示出标准误差估计的优异性能,特别是分散参数.
- 对口腔阅读流度 (ORF) 数据的分析显示出显著的物品水平分散差异.
- 与标准模型相比,Beta双项模型提供了更好的匹配,SRMSR值证实了这一点.
结论:
- 开发的联合计时模型有效地捕捉了与准确性和速度相关的潜在特征.
- 在这种情况下,Beta-二项式分布对于模拟过度分散的计数数据是有利的.
- 在复杂模型中重新采样是一种可靠的估计标准误差的方法.
- 该方法为分析复杂的测量数据提供了有价值的工具,如ORF数据所示.
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