Blázquez-Rincón Desirée, López-López José Antonio, Viechtbauer Wolfgang
Department of Psychology, Universidad a Distancia de Madrid, Madrid, Spain.
Department of Basic Psychology and Methodology, University of Murcia, Murcia, Spain.
Behav Res Methods. 2025 Mar 17;57(4):118. doi: 10.3758/s13428-025-02622-5.
Location-scale models in the field of meta-analysis allow researchers to simultaneously study the influence of moderator variables on the mean (location) and variance (scale) of the distribution of true effects. However, the increased complexity of such models can make model fitting challenging. Moreover, the statistical properties of the estimation and inference methods for such models have not been systematically examined in the meta-analytic context. We therefore conducted a Monte Carlo simulation study to compare different estimation methods (maximum or restricted maximum likelihood estimation), significance tests (Wald-type, permutation, and likelihood-ratio tests), and methods for constructing confidence intervals (Wald-type and profile-likelihood intervals) for the scale coefficients of such models. When restricted maximum likelihood estimation was used, slightly closer to nominal rejection rates and narrower confidence intervals were obtained. The permutation test yielded type I error rates closest to the nominal level, whereas the likelihood-ratio test obtained the highest statistical power. In most scenarios, profile-likelihood intervals showed lower coverage probabilities than the Wald-type method but closer to the nominal 95% level. Finally, slightly higher rejection rates and coverage probabilities were obtained when a dichotomous moderator was examined rather than a continuous one. Despite the need to use some constraints on the parameter space for the scale coefficients and the possibility of non-convergence of some procedures that may affect the fitting of the specified models, location-scale models proved to be a valid and useful tool for modeling the heterogeneity parameter in meta-analysis.
元分析领域中的位置 - 尺度模型使研究人员能够同时研究调节变量对真实效应分布的均值（位置）和方差（尺度）的影响。然而，此类模型复杂性的增加可能会使模型拟合具有挑战性。此外，在此类模型的估计和推断方法的统计特性在元分析背景下尚未得到系统检验。因此，我们进行了一项蒙特卡罗模拟研究，以比较不同的估计方法（最大或限制最大似然估计）、显著性检验（ Wald 型、置换和似然比检验）以及为此类模型的尺度系数构建置信区间的方法（ Wald 型和轮廓似然区间）。当使用限制最大似然估计时，得到的结果略接近名义拒绝率且置信区间更窄。置换检验产生的 I 型错误率最接近名义水平，而似然比检验获得的统计功效最高。在大多数情况下，轮廓似然区间的覆盖概率低于 Wald 型方法，但更接近名义 95% 水平。最后，当检验二分调节变量而非连续调节变量时，获得的拒绝率和覆盖概率略高。尽管需要对尺度系数的参数空间使用一些约束，并且某些程序可能存在不收敛的可能性，这可能会影响指定模型的拟合，但位置 - 尺度模型被证明是在元分析中对异质性参数进行建模的有效且有用的工具。
