This paper studies the influence diagnostics in meta‐regression model including case deletion diagnostic and local influence analysis. We derive the subset deletion formulae for the estimation of regression coefficient and heterogeneity variance and obtain the corresponding influence measures. The DerSimonian and Laird estimation and maximum likelihood estimation methods in meta‐regression are considered, respectively, to derive the results. Internal and external residual and leverage measure are defined. The local influence analysis based on case‐weights perturbation scheme, responses perturbation scheme, covariate perturbation scheme, and within‐variance perturbation scheme are explored. We introduce a method by simultaneous perturbing responses, covariate, and within‐variance to obtain the local influence measure, which has an advantage of capable to compare the influence magnitude of influential studies from different perturbations. An example is used to illustrate the proposed methodology.

中文翻译：

---

元回归模型中的影响诊断。

本文研究了元回归模型中的影响诊断，包括案例删除诊断和局部影响分析。我们推导了子集删除公式，用于估计回归系数和异质性方差，并获得相应的影响度量。分别考虑了元回归中的DerSimonian和Laird估计以及最大似然估计方法来得出结果。定义了内部和外部残差和杠杆措施。探索了基于案例权重扰动方案，响应扰动方案，协变量扰动方案和方差内扰动方案的局部影响分析。我们引入了一种通过同时扰动响应，协变量和方差来获得局部影响力度量的方法，它的优点是能够比较来自不同扰动的影响研究的影响程度。举一个例子来说明所提出的方法。