在高斯混合模型下估计IRT模型 隐藏特征的建模:MSAEM算法的应用
1School of Mathematics and Statistics, KLAS, Northeast Normal University, Changchun, Jilin Province, China.
Multivariate behavioral research
|June 8, 2025
概括
在物品响应理论 (IRT) 中的潜伏特征的高斯混合模型 (GMM) 提高了准确性. 一个新的混合随机近似EM算法 (MSAEM) 可靠地估计GMM-IRT模型,克服计算挑战.
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:
- 项目响应理论 (IRT) 通常假设潜伏特征的正常分布,这往往不充分反映复杂的数据.
- 在IRT中违反正常性可能导致不准确的统计推断.
- 高斯混合模型 (GMM) 为模拟IRT (GMM-IRT) 中的潜在特征异质提供了一个灵活的替代方案.
研究的目的:
- 为物品响应理论 (GMM-IRT) 中高斯混合模型提出可靠和强大的计算方法.
- 解决阻碍GMM-IRT模型广泛应用的计算挑战.
- 开发一个算法来估计三参数正常形模型与GMM的潜伏特征 (GMM-3PNO).
主要方法:
- 开发用于GMM-3PNO估计的混合随机近似EM (MSAEM) 算法.
- 将GMM-3PNO模型扩展为指数家族内的完整数据模型,以简化计算.
- 在MSAEM算法中实施策略,以防止标签交换并确保趋同.
主要成果:
- 拟议的MSAEM算法为估计GMM-IRT模型提供了一个强大的和高效的方法.
- 与GMM-IRT估计相关的计算负担大大减少.
- 模拟和经验研究证实了MSAEM算法的有效性和GMM-IRT模型的优势.
结论:
- MSAEM算法为估计复杂的GMM-IRT模型提供了一个实际的解决方案.
- GMM-IRT模型有效地捕捉潜伏特征异质性,从而得出更准确的推断.
- 开发的方法有助于在各个领域更广泛地采用先进的IRT模型.
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