Generalized Least Squares F Test in Regression Analysis With Two-Stage Cluster Samples
两阶段整群抽样回归分析中的广义最小二乘 F 检验AI 解读 ↓
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两阶段整群抽样回归分析中的广义最小二乘 F 检验
- 研究问题
- 两阶段整群抽样导致组内误差相关时，如何构造回归 F 检验，使其控制第一类错误率并改善对备择的检验功效？
- 方法与思路
- 作者先用 Henderson 的拟合常数法估计共同组内相关系数，再将其代入已知相关系数情况下的 GLS F 统计量。
- 材料陈述的贡献
- 摘要称，模拟中两步 GLS 检验在小相关程度下也能达到校正 F 检验的尺寸控制，并在较大相关程度下获得功效增益。
- 阅读关注点
- 应核对共同组内相关的模型限制、相关系数估计和检验实现，以及模拟覆盖的群数、群大小和原假设维数。
- 阅读边界
- 摘要未给出模拟设计和增益数值，不能推广至任意聚类结构；提及的相关符号不一致，公式需核对原文。索引摘要版本未注明。
原文摘要
When data are obtained by two-stage cluster sampling, serious problems can arise if conventional methods that ignore the intracluster correlations are used. Wu, Holt, and Holmes showed that the standard F statistic in regression analysis leads to inflated type I error rate (or size) due to correlated errors in the regression model appropriate for clustered data. They proposed a simple correction to the standard F statistic that takes into account common intracluster correlation, p, and showed, through simulation, that the corrected F test performs much better than the standard F test in controlling the size for a scalar hypothesis. It also performed almost as well as an iterative generalized least squares (IGLS) F statistic for large values of ρ and better than the IGLS for small ρ in controlling the size. This article considers a two-step generalized least squares (GLS) F statistic by first estimating ρ, using the well-known method of fitting constants due to Henderson, and then substituting the estimate into the GLS test statistic when ρ is known. It is shown, through simulation, that the GLS F statistic performs as well as the corrected F statistic in controlling the size even for small ρ, and at the same time leads to significant power gains over the corrected F for larger values of ρ.