Equivalences between ad hoc strategies and meta-analytic models for dependent effect sizes

Meta-analyses of educational research findings frequently involve statistically dependent effect size estimates. Meta-analysts have often addressed dependence issues using ad hoc approaches that involve modifying the data to conform to the assumptions of models for independent effect size estimates, such as aggregating estimates to obtain one summary estimate per study, conducting separate analyses of distinct subgroups of estimates, or combinations thereof. We demonstrate that these ad hoc approaches correspond exactly to certain multivariate models for dependent effect sizes. Specifically, we describe classes of multivariate random effects models that have likelihoods equivalent to those of models for effect sizes that have been averaged by study, classified into subgroups, or both. The equivalence also applies to robust variance estimation methods.

教育研究结果的元分析通常涉及对统计上相互依赖的效应量估计。元分析者常采用临时措施来解决依赖性问题，这些措施包括调整数据以符合独立效应量估计模型的假设，例如通过对每个研究进行汇总估计以获得单一总结估计，对估计的不同子组进行单独分析，或二者结合。我们证明这些临时措施与某些针对依赖效应量的多元模型完全对应。具体而言，我们描述了具有与通过研究平均、分类为子组或两者兼而有之的效应量模型相等的似然函数的多元随机效应模型类别。这种等价性也适用于稳健方差估计方法。