使用连续离散延长卡尔曼波器的连续时间模型估计非线性混合效应
Lu Ou1, Michael D Hunter1, Zhaohua Lu1
1The Pennsylvania State University, State College, Pennsylvania, USA.
The British journal of mathematical and statistical psychology
|September 7, 2023
概括
本研究探讨了使用连续离散扩展卡尔曼波器 (CDEKF) 适配非线性混合效应随机微分方程 (SDE) 模型. 这种方法在满足识别约束条件时显示出分析复杂的纵向数据的前景.
科学领域:
- 统计 统计 统计 统计
- 量化心理学 量化心理学
- 计算神经科学是一种神经科学.
背景情况:
- 密集的纵向数据通常会在不规则的间隔内显示复杂,非线性和异质的变化模式.
- 建模此类数据需要连续时间微分方程模型,潜在的非线性和混合效应.
- 目前适应混合效应随机微分方程 (SDE) 模型的方法,特别是使用连续离散扩展卡尔曼波器 (CDEKF),缺乏关于有效性和识别约束的彻底调查.
研究的目的:
- 通过CDEKF方法,通过分析检查适配非线性混合效应SDE模型的识别约束.
- 将已发表的情感模型扩展为非线性混合效应SDE框架,并将其应用于生态瞬间评估 (EMA) 数据.
- 通过蒙特卡洛模拟来评估拟议的CDEKF方法的可行性,以通过蒙特卡洛模拟来装配这些复杂的模型.
主要方法:
- 对配备CDEKF的非线性混合效应SDE模型的识别约束的分析检查.
- 将现有的情感模型扩展到非线性混合效应SDE框架.
- 扩展模型应用于不规则间隔的EMA数据,并通过蒙特卡洛模拟研究进行验证.
主要成果:
- 拟议的CDEKF方法为非线性混合效应SDE模型产生合理的参数和标准误差估计,前提是满足某些识别约束.
- 模拟研究表明,在不同的条件下,这种方法的可行性.
- 该研究调查了样本大小,工艺噪声差异和数据间距对估计结果的影响.
结论:
- 连续离散扩展卡尔曼波器 (CDEKF) 方法是一种可行的方法,用于将非线性混合效应随机微分方程 (SDE) 模型与密集的纵向数据相匹配.
- 满足特定的识别约束对于可靠的参数估计至关重要.
- 这些发现为研究人员提供了有价值的见解,研究人员用不规则的采样数据建模复杂的动态过程.
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