Faculty of Psychology and Educational Sciences, University of Leuven, Vesaliusstraat 2, 3000, Leuven, Belgium.
Behav Res Methods. 2013 Jun;45(2):576-94. doi: 10.3758/s13428-012-0261-6.
Although dependence in effect sizes is ubiquitous, commonly used meta-analytic methods assume independent effect sizes. We describe and illustrate three-level extensions of a mixed effects meta-analytic model that accounts for various sources of dependence within and across studies, because multilevel extensions of meta-analytic models still are not well known. We also present a three-level model for the common case where, within studies, multiple effect sizes are calculated using the same sample. Whereas this approach is relatively simple and does not require imputing values for the unknown sampling covariances, it has hardly been used, and its performance has not been empirically investigated. Therefore, we set up a simulation study, showing that also in this situation, a three-level approach yields valid results: Estimates of the treatment effects and the corresponding standard errors are unbiased.
尽管依赖于效应大小是普遍存在的，但常用的元分析方法假设效应大小是独立的。我们描述并说明了混合效应元分析模型的三个层次扩展，该模型考虑了研究内和研究间各种来源的依赖关系，因为元分析模型的多层次扩展仍然不为人知。我们还提出了一个三级模型，用于常见的情况，即研究内，使用相同的样本计算多个效应大小。虽然这种方法相对简单，并且不需要对未知抽样协方差进行插补值，但几乎没有使用过，其性能也没有经过实证研究。因此，我们进行了一项模拟研究，表明在这种情况下，三级方法也能得到有效的结果：处理效果的估计值和相应的标准误差是无偏的。
