An unobserved random effect is often used to describe the between‐study variation that is apparent in meta‐analysis datasets. A normally distributed random effect is conventionally used for this purpose. When outliers or other unusual estimates are included in the analysis, the use of alternative random effect distributions has previously been proposed. Instead of adopting the usual hierarchical approach to modelling between‐study variation, and so directly modelling the study specific true underling effects, we propose two new marginal distributions for modelling heterogeneous datasets. These two distributions are suggested because numerical integration is not needed to evaluate the likelihood. This makes the computation required when fitting our models much more robust. The properties of the new distributions are described, and the methodology is exemplified by fitting models to four datasets. © 2015 The Authors. Research Synthesis Methods published by John Wiley & Sons, Ltd.

中文翻译：

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用于描述元分析中异常值的新模型。

未观察到的随机效应通常用于描述元分析数据集中明显的研究间变异。为此目的通常使用正态分布的随机效应。当分析中包含异常值或其他不寻常的估计值时，先前已提出使用替代随机效应分布。我们没有采用通常的分层方法来建模研究之间的变化，而是直接对研究特定的真实基础效应进行建模，而是提出了两种新的边际分布来建模异构数据集。建议使用这两种分布，因为不需要数值积分来评估可能性。这使得拟合我们的模型时所需的计算更加稳健。描述了新分布的属性，该方法通过将模型拟合到四个数据集来举例说明。© 2015 作者。研究合成方法由 John Wiley & Sons, Ltd. 出版。