The Effect of Two-Stage Sampling on the F Statistic
两阶段抽样对 F 统计量的影响AI 解读 ↓
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两阶段抽样对 F 统计量的影响
- 研究问题
- 两阶段调查抽样中的组内相关会怎样扭曲普通回归的 F 检验，如何诊断这种影响并在组内相关未知时作出修正？
- 方法与思路
- 作者构造诊断度量，按回归变量及其交叉乘积分解相关影响，并提出无需迭代的 F 检验修正，以理论、数值和模拟评估。
- 材料陈述的贡献
- 摘要称，诊断度量能解释组内相关引起的 F 统计量扭曲；所提修正在模拟中至少不逊于广义最小二乘方法，计算步骤较简单。
- 阅读关注点
- 应核对两阶段抽样与组内相关模型、诊断分解和修正公式、未知相关性的估计方式，以及与广义最小二乘比较的指标。
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- 仅据稿件版本未注明的 OpenAlex 索引摘要；具体模型条件、修正公式和模拟范围未提供，不能将所述比较推广至任意聚类数据。
原文摘要
The assumption of iid observations that underlies many statistical procedures is called into question when analyzing complex survey data. The population structure—particularly the existence of clusters in two-stage samples that usually exhibit positive intracluster correlation—invalidates the independence assumption. Kish and Frankel (1974) investigated the impact of this fact on regression analysis by using the standard sample-survey-theory framework; Campbell (1977) and Scott and Holt (1982) used the linear model framework. In general, although ordinary least squares (OLS) procedures are unbiased but not fully efficient for estimation of the regression coefficients, serious difficulties can arise when using OLS estimators for second-order terms. Variances of the OLS estimators for the regression coefficients can be larger (sometimes much larger) than the usual OLS variance expression would indicate. Failure to consider this possibility leads to underestimation of variances, with consequences for confidence intervals. This article follows this effect through to the F statistic, because of its importance to hypothesis tests and confidence ellipsoids. Our major aim is to investigate the effect of intracluster correlation on the F statistic. We propose a diagnostic measure identifying when the ordinary F statistic is likely to be affected and give decomposition in terms of the contributions of the individual regressors and their cross-products, based on a similar decomposition for the projection matrix in Appendix A. We establish numerically and theoretically the effectiveness of this measure in understanding the degree of distortion of F by intracluster correlation. The measure leads to a correction for the F test for unknown intracluster correlation. This is a slightly simpler numerical procedure than the generalized least squares (GLS), since it does not require iteration. The correction is shown to perform at least as well as the GLS in a simulation study.