用拉普拉斯近似方法对具有模式共变矩阵的等级通用线性混合模型进行边际推理.
Jay M Ver Hoef1, Eryn Blagg2, Michael Dumelle3
1Marine Mammal Laboratory, NOAA-NMFS Alaska Fisheries Science Center, Seattle, Washington, USA.
Environmetrics
|December 31, 2024
概括
我们为具有复杂共变性结构的通用线性混合模型提供了一种快速,全参数的方法. 这种方法使完全的边际推断和预测成为可能,优于贝叶斯方法,并提供比INLA更大的灵活性.
科学领域:
- 统计 统计 统计 统计
- 计算统计学 计算统计学
- 统计建模 统计建模
背景情况:
- 通用线性混合模型 (GLMM) 对于分析复杂数据结构至关重要.
- 现有的用模式共变矩阵估计GLMM的方法可能是计算密集的或范围有限的.
- 完全参数化的方法提供了一个强大的框架,但需要高效的估计技术.
研究的目的:
- 为GLMMs开发一个完全参数的,分层的建模框架,容纳任何模式共变矩阵.
- 为了实现完整的边际推断,包括参数的估计和未观察到的数据的预测.
- 为现有方法提供一个计算效率高和可通用的替代方案.
主要方法:
- 使用拉普拉斯近似来通过整合固定和潜在的随机效应来对协差参数进行边际估计.
- 使用牛顿-拉普森更新来估计参数和预测潜在的随机效应.
- 开发了六种常见分布 (二进制,计数,正连续) 的边际概率,并证明了可扩展性.
主要成果:
- 提出的方法在偏差,预测错误和间隔覆盖率方面取得了与完全贝叶斯方法,自动分化和集成嵌套拉普拉斯近似 (INLA) 相当的结果.
- 与贝叶斯方法相比,开发的参数方法显示了显著更快的计算时间.
- 该框架被证明比INLA更为通用,处理了更广泛的模式共变性结构.
结论:
- 基于拉普拉斯近似的全参数方法为具有模式共变性的GLMM提供了一种高效和多功能方法.
- 这种方法在各种数据类型和复杂结构中提供了完整的边际推理和预测.
- 开发的框架为统计建模提供了一个有价值的,更快速,更普遍的替代方案.
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