一个统一的EM框架用于估计和推断正常的ogive项目响应模型
1KLAS, Key Laboratory of Big Data Analysis of Jilin Province, School of Mathematics and Statistics, Northeast Normal University, Changchun, China.
The British journal of mathematical and statistical psychology
|October 10, 2024
概括
本研究介绍了一种高效的预期最大化 (EM) 算法,用于在物品响应理论 (IRT) 中估计正常导向 (NO) 模型. 新方法提高了教育和心理测量的计算效率和可靠性.
科学领域:
- 心理测量 心理测量 心理测量
- 教育测量教育的测量
- 统计建模 统计建模
背景情况:
- 正常的Ogive (NO) 模型是物品响应理论 (IRT) 的组成部分.
- 对NO模型的参数估计带来了重大的计算挑战.
- 现有的方法在参数估计中往往缺乏效率和可靠性.
研究的目的:
- 开发一种高效,可靠的计算方法,用于适配正常导弹 (NO) 模型.
- 为NO模型估计引入一种新的,统一的预期最大化 (EM) 算法.
- 为了解决与NO模型参数估计相关的计算困难.
主要方法:
- 建议使用统一的预期最大化 (EM) 算法来估计两个,三个和四个参数的NO模型.
- 该算法将NO模型扩大为指数家族内的完整数据模型,简化了EM代.
- 为了减少集成维度,在E步骤中引入了一种两步期望程序,同时还引入了一种标准错误估计方法.
主要成果:
- 模拟研究表明,拟议的算法提供了卓越的恢复精度,稳定性和计算效率.
- 该方法有效地处理各种NO模型参数的估计.
- 国际学生评估计划 (PISA) 数据的应用证实了参数估计的可靠性.
结论:
- 新的EM算法为估计正常形模型提供了高效和可靠的解决方案.
- 该方法通过避免M步数值优化和减少E步的集成维度来简化计算.
- 经过验证的方法增强了IRT在教育和心理测量的实际应用.
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