对混合效应的模型选择 位置尺度模型与LOO或WAIC差异的置信区间
Yue Liu1, Fan Fang2, Hongyun Liu3,4
1Institute of Brain and Psychological Sciences, Sichuan Normal University, Chengdu, China.
Multivariate behavioral research
|February 18, 2025
概括
使用置信区间的顺序方法提高了贝叶斯模型选择准确性,用于混合效应的位置尺度模型 (MELSMs),而不是点估计. 这种方法可以提高模型的性能,特别是在更简单的模型或更大的样本大小的情况下.
科学领域:
- 贝叶斯统计学 贝叶斯统计学
- 统计建模 统计建模
- 计量经济学 计量经济学 计量经济学
背景情况:
- 交叉验证 (LOO) 和广泛适用的信息标准 (WAIC) 是贝叶斯模型选择的标准.
- 目前的做法往往依赖于点估计,忽视了模型合适指数固有的不确定性.
- 这种监督会导致在复杂的统计分析中做出低于最佳的模型选择.
研究的目的:
- 介绍和评估一个新的序列方法,用于贝叶斯模型比较.
- 拟议的方法使用LOO或WAIC的置信区间,解决点估计中的不确定性.
- 评估这种顺序方法在选择混合效应位置尺度模型 (MELSMs) 的有效性.
主要方法:
- 一项模拟研究旨在将拟议的顺序方法与传统的点估计方法进行比较.
- 重点是选择合适的混合效应位置规模模型 (MELSM).
- 使用信心区间 (具体为90%) 来评估适应指数 (LOO和WAIC).
主要成果:
- 顺序方法在特定条件下 (简单的真实模型,规模模型中的大型随机拦截,大样本大小) 与点方法相比,显示出更高的模型选择精度.
- 通过顺序方法选择的模型表现出更好的统计特性:更高的功率,更窄的可信区间,固定效应的标准误差减少,随机效应的偏差更低.
- 只有在小的1级样本大小中才出现LOO和WAIC之间的显著差异,在均或异质残余差异的情况下有利于LOO.
结论:
- 序列模型比较方法,利用置信区间,为MELSMs的贝叶斯模型选择提供了更强大的方法.
- 这种技术通过考虑估计不确定性来提高模型选择的可靠性.
- 这些发现为使用贝叶斯统计学的研究人员提供了宝贵的指导,特别是在处理混合效应模型时.
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