贝叶斯对纵向多组IRT数据的贝叶斯建模,具有扭曲的潜分布和增长曲线
José Roberto Silva Dos Santos1, Caio Lucidius Naberezny Azevedo2, Jean-Paul Fox3
1Department of Statistics and Applied Mathematics, Federal University of Ceara, Fortaleza, Brazil.
Multivariate behavioral research
|April 10, 2025
概括
这项研究引入了一个新的纵向物件响应理论 (IRT) 模型,以更好地分析倾斜的数据. 这种先进的模型准确地捕捉了随着时间的推移潜伏特征中的复杂模式,提高了测量准确性.
科学领域:
- 心理测量 心理测量 心理测量
- 统计建模 统计建模
- 纵向数据分析 纵向数据分析
背景情况:
- 传统的纵向物件响应理论 (IRT) 模型通常假设正常分布的潜伏特征.
- 现有的模型可能无法充分捕捉随时间推移的特征分布中的不对称性或斜率.
- 需要更灵活的IRT模型来处理纵向研究中的非正常潜伏特征模式.
研究的目的:
- 引入一种新的多组纵向IRT模型,能够处理偏斜的潜在特征分布.
- 扩大Santos等人提出的纵向IRT模型的一般类别. (2022年) 的第二季.
- 为表现不对称潜伏特征模式的纵向数据提供更准确的测量框架.
主要方法:
- 拟议的模型采用多变量斜正态分布的潜伏特征,结合一个反依赖结构与中心的斜正态错误.
- 隐性平均轨迹是用二次曲线建模的,结构化协差矩阵捕捉参与者之间的依赖关系.
- 混合马尔科夫链蒙特卡洛 (MCMC) 算法,结合FFBS采样器和大都市-哈斯廷斯步骤,用于贝叶斯参数估计和模型合适性评估.
主要成果:
- 该模型有效地捕捉了潜在特征中的不对称性,在真实数据应用中表现优于传统的正常模型.
- 一项模拟研究表明,在各种条件下,模型的稳定性得到了证明.
- 对GERES项目数据的应用凸显了在纵向IRT中计算偏差分布的实际实用性.
结论:
- 开发的多组纵向IRT模型为分析具有倾斜隐性特征分布的数据提供了重大进步.
- 这种方法提高了纵向研究中心理测量建模的准确性和灵活性.
- 该模型为研究人员提供了一种有价值的工具,研究发展过程或随时间变化而发生的潜在特征可能不会正常分布的变化.
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