An Exact Bayesian Model for Meta-Analysis of the Standardized Mean Difference with Its Simultaneous Credible Intervals.

IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Multivariate Behavioral Research Pub Date : 2024-09-01 Epub Date: 2024-07-23 DOI:10.1080/00273171.2024.2358233
Yonggang Lu, Qiujie Zheng, Kevin Henning
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Abstract

While Bayesian methodology is increasingly favored in behavioral research for its clear probabilistic inference and model structure, its widespread acceptance as a standard meta-analysis approach remains limited. Although some conventional Bayesian hierarchical models are frequently used for analysis, their performance has not been thoroughly examined. This study evaluates two commonly used Bayesian models for meta-analysis of standardized mean difference and identifies significant issues with these models. In response, we introduce a new Bayesian model equipped with novel features that address existing model concerns and a broader limitation of the current Bayesian meta-analysis. Furthermore, we introduce a simple computational approach to construct simultaneous credible intervals for the summary effect and between-study heterogeneity, based on their joint posterior samples. This fully captures the joint uncertainty in these parameters, a task that is challenging or impractical with frequentist models. Through simulation studies rooted in a joint Bayesian/frequentist paradigm, we compare our model's performance against existing ones under conditions that mirror realistic research scenarios. The results reveal that our new model outperforms others and shows enhanced statistical properties. We also demonstrate the practicality of our models using real-world examples, highlighting how our approach strengthens the robustness of inferences regarding the summary effect.

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用于标准化均值差及其同时可信区间元分析的精确贝叶斯模型。
尽管贝叶斯方法因其明确的概率推断和模型结构而在行为学研究中日益受到青睐,但作为一种标准的荟萃分析方法,其被广泛接受的程度仍然有限。虽然一些传统的贝叶斯分层模型经常被用于分析,但它们的性能尚未得到深入研究。本研究评估了两种常用的用于标准化均值差异元分析的贝叶斯模型,发现了这些模型存在的重大问题。为此,我们引入了一种新的贝叶斯模型,该模型具有新颖的特点,可解决现有模型存在的问题以及当前贝叶斯荟萃分析存在的更广泛的局限性。此外,我们还引入了一种简单的计算方法,根据汇总效应和研究间异质性的联合后验样本,同时构建它们的可信区间。这充分体现了这些参数的共同不确定性,而频繁主义模型的这一任务具有挑战性或不切实际。通过基于贝叶斯/频数模型联合范式的模拟研究,我们比较了我们的模型与现有模型在反映现实研究场景条件下的性能。结果表明,我们的新模型优于其他模型,并显示出更强的统计特性。我们还利用现实世界的例子证明了我们的模型的实用性,强调了我们的方法如何加强了有关总结效应推断的稳健性。
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来源期刊
Multivariate Behavioral Research
Multivariate Behavioral Research 数学-数学跨学科应用
CiteScore
7.60
自引率
2.60%
发文量
49
审稿时长
>12 weeks
期刊介绍: Multivariate Behavioral Research (MBR) publishes a variety of substantive, methodological, and theoretical articles in all areas of the social and behavioral sciences. Most MBR articles fall into one of two categories. Substantive articles report on applications of sophisticated multivariate research methods to study topics of substantive interest in personality, health, intelligence, industrial/organizational, and other behavioral science areas. Methodological articles present and/or evaluate new developments in multivariate methods, or address methodological issues in current research. We also encourage submission of integrative articles related to pedagogy involving multivariate research methods, and to historical treatments of interest and relevance to multivariate research methods.
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