Motivated by the self-thinning meta-data, a randomeffects meta-analysis model with unknown precision parameters is proposed with a truncated Poisson regression model for missing sample sizes. The random effects are assumed to follow a heavy-tailed distribution to accommodate outlying aggregate values in the response variable. The logarithm of the pseudo-marginal likelihood (LPML) is used for model comparison. In addition, in order to determine which selfthinning law is more supported by the meta-data, a measure called “Plausibility Index (PI)” is developed. A simulation study is conducted to examine empirical performance of the proposed methodology. Finally, the proposed model and the PI measure are applied to analyze a self-thinning meta-data set in details.

中文翻译：

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贝叶斯元回归模型使用重尾随机效应和缺失样本大小的自稀疏元数据

受自精简元数据的启发，提出了一种具有未知精度参数的随机效应元分析模型，其中包含用于缺失样本量的截断泊松回归模型。假设随机效应遵循重尾分布，以适应响应变量中的异常聚合值。伪边际似然 (LPML) 的对数用于模型比较。此外，为了确定元数据更支持哪种自稀疏定律，开发了一种称为“合理性指数（PI）”的度量。进行模拟研究以检查所提出方法的经验性能。最后，将所提出的模型和 PI 度量应用于详细分析自精简元数据集。