Manuel Suero, Juan Botella, Juan I Duran, Desirée Blazquez-Rincón
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引用次数: 0
摘要
经典的元分析随机效应模型(meta-analytical random effects model, REM)在处理标准化平均差(standard mean difference, g)时存在一些缺陷。从本质上讲,所涉及的研究的方差被视为条件方差,并给定一个δ值,而不是无条件方差。因此,方差的估计涉及到g值与其方差之间的依赖关系,从而扭曲了估计。经典的REM是用线性模型表示的,g的方差是通过方差分量的框架得到的。尽管REM的弱点在实际情况中可以忽略不计,但总的来说,它们构成了元分析随机效应模型的近似简化版本。我们提出了一种替代公式,作为混合模型,并提供了g的边际分布的期望值、方差和偏度的公式。蒙特卡罗模拟支持了公式的准确性。然后,提出了真实效应的均值和方差的无偏估计,并通过蒙特卡罗模拟进行了评估。讨论了混合模型公式相对于“经典”公式的优点。
Reformulating the meta-analytical random effects model of the standardized mean difference as a mixture model.
The classical meta-analytical random effects model (REM) has some weaknesses when applied to the standardized mean difference, g. Essentially, the variance of the studies involved is taken as the conditional variance, given a δ value, instead of the unconditional variance. As a consequence, the estimators of the variances involve a dependency between the g values and their variances that distorts the estimates. The classical REM is expressed as a linear model and the variance of g is obtained through a framework of components of variance. Although the weaknesses of the REM are negligible in practical terms in a wide range of realistic scenarios, all together, they make up an approximate, simplified version of the meta-analytical random effects model. We present an alternative formulation, as a mixture model, and provide formulas for the expected value, variance and skewness of the marginal distribution of g. A Monte Carlo simulation supports the accuracy of the formulas. Then, unbiased estimators of both the mean and the variance of the true effects are proposed, and assessed through Monte Carlo simulations. The advantages of the mixture model formulation over the "classical" formulation are discussed.
期刊介绍:
Behavior Research Methods publishes articles concerned with the methods, techniques, and instrumentation of research in experimental psychology. The journal focuses particularly on the use of computer technology in psychological research. An annual special issue is devoted to this field.