On the Hauck–Donner Effect in Wald Tests: Detection, Tipping Points, and Parameter Space Characterization
Wald 检验中的 Hauck–Donner 效应：检测、临界点与参数空间刻画AI 解读 ↓
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Wald 检验中的 Hauck–Donner 效应：检测、临界点与参数空间刻画
- 研究问题
- 为何参数估计越远离零假设，Wald 统计量反而可能不再增大，并导致偏高的 p 值和功效损失；如何检测与刻画这种现象？
- 方法与思路
- 作者在向量广义线性模型中构造效应检测方法，以 Wald、得分和似然比统计量的比值刻画单参数大样本情形并划分严重程度。
- 材料陈述的贡献
- 摘要称，论文提出检测与分级结果，并证明二乘二列联表中出现该效应的必要条件为对数优势比至少为二，同时给出实践建议。
- 阅读关注点
- 应核对统计量非单调性的定义、检测方法的适用模型、严重程度分界，以及列联表阈值作为必要条件的准确范围。
- 阅读边界
- 依据版本未注明的 OpenAlex 索引摘要；具体检测公式与分级边界未提供，所报列联表阈值是必要条件，不能当作充分条件或通用阈值。
原文摘要
The Wald test remains ubiquitous in statistical practice despite shortcomings such as its inaccuracy in small samples and lack of invariance under reparameterization. This article develops on another but lesser-known shortcoming called the Hauck–Donner effect (HDE) whereby a Wald test statistic is no longer monotone increasing as a function of increasing distance between the parameter estimate and the null value. Resulting in an upward biased p-value and loss of power, the aberration can lead to very damaging consequences such as in variable selection. The HDE afflicts many types of regression models and corresponds to estimates near the boundary of the parameter space. This article presents several new results, and its main contributions are to (i) propose a very general test for detecting the HDE in the class of vector generalized linear models (VGLMs), regardless of the underlying cause; (ii) fundamentally characterize the HDE by pairwise ratios of Wald and Rao score and likelihood ratio test statistics for 1-parameter distributions with large samples; (iii) show that the parameter space may be partitioned into an interior encased by at least 5 HDE severity measures (faint, weak, moderate, strong, extreme); (iv) prove that a necessary condition for the HDE in a 2 by 2 table is a log odds ratio of at least 2; (v) give some practical guidelines about HDE-free hypothesis testing. Overall, practical post-fit tests can now be conducted potentially to any model estimated by iteratively reweighted least squares, especially the GLM and VGLM classes, the latter which encompasses many popular regression models.