基于贝叶斯模型平均的元分析：原理与实现
Meta-Analysis Based on Bayesian Model Averaging: Principles and Implementation
任子伟 1刘铮 2胡传鹏1
作者信息
- 1. 南京师范大学
- 2. 香港中文大学(深圳)
- 折叠
摘要
元分析作为一种综合已有研究成果的重要统计方法，在量化研究中广泛应用。然而，研究者在分析过程中常面临模型选择的困境：在处理研究间异质性时，需在固定效应与随机效应模型之间做出选择；在应对潜在发表偏倚时，又需要从多种校正模型中选定一种。目前，这些模型选择仍缺乏统一标准。贝叶斯统计框架下的贝叶斯模型平均(Bayesian Model Averaging, BMA)为解决这些问题提供了新的思路：它将不同统计模型纳入同一模型空间，量化各模型获得数据支持的程度，并据此对效应量进行加权，从而规避单一模型选择带来的不确定性。基于BMA的元分析能同时检验三个关键假设(效应是否存在、异质性是否存在以及发表偏倚是否存在)，并以模型平均的方式实现对效应量的稳健估计。该方法可通过开源软件 JASP 或 R 语言实现，为研究者实施元分析提供了新选择。
Abstract
Meta-analysis serves as an essential statistical methodology to synthesize independent empirical findings. It is deeply embedded across various quantitative disciplines. However, researchers routinely confront significant dilemmas regarding model selection throughout the analytical workflow. When managing across-study heterogeneity, researchers face a strict choice between fixed-effects and random-effects frameworks. Similarly, to mitigate the threat of potential publication bias, researchers choose from a diverse array of disparate correction models. At present, the field lacks a unified, standardized criterion for selecting the single optimal model configuration. Consequently, traditional approaches rely on a single chosen model and neglect model uncertainty. This omission causes overconfident statistical inferences, underestimated standard errors, and potentially biased estimates of the true population effect size. In turn, these estimation errors reduce the replicability of empirical findings.To resolve these deep-seated methodological vulnerabilities, Bayesian Model Averaging (BMA) offers an innovative and mathematically rigorous paradigm that operates within the broader Bayesian statistical framework. Instead of an arbitrary, ex-ante selection of a single statistical model, BMA directly accommodates model uncertainty. It embeds all theoretically plausible candidate models into a single, cohesive model space. Specifically, BMA treats the model itself as a random variable within a probability space. This formulation effectively manages uncertainty in both the effect size and heterogeneity. By establishing prior probabilities for each model configuration, BMA leverages empirical data to calculate posterior model probabilities. This process quantifies the precise degree of empirical data support that each individual model receives. Ultimately, the final effect size is a weighted average across all models, where posterior probabilities directly determine individual model weights. This approach avoids the inherent biases of single-model selection. It yields a continuous measure of cumulative evidence rather than a binary accept-reject decision.Researchers operationalize this rigorous approach in meta-analysis as robust Bayesian meta-analysis (RoBMA). RoBMA inherits the core model-averaging principles of BMA. It systematically incorporates multiple publication bias correction models, such as selection models and PET-PEESE (precision-effect test and precision-effect estimate with standard error), into the Bayesian inference framework. It avoids a forced selection of a single optimal model. Instead, the framework weights competing hypotheses within the model space based directly on empirical data. This mechanism provides rigorous quantitative evidence, specifically inclusion Bayes factors (BF), to evaluate 3 critical hypotheses concurrently to govern the validity of literature synthesis. These hypotheses test whether a true population effect exists, whether study-level heterogeneity is present, and whether publication bias contaminates the literature. RoBMA constructs a multi-dimensional model space to map every possible combination of these 3 dimensions (e.g., presence vs. absence of an effect, presence vs. absence of heterogeneity, and presence vs. absence of publication bias). As a consequence, the framework outputs model-averaged posterior estimates that fully incorporate model uncertainty, delivering an exceptionally robust and reliable evaluation of the primary effect size. Beyond its conceptual and theoretical advantages, the practical execution of BMA-based meta-analysis has become highly viable due to contemporary computational breakthroughs and software integration. This paper comprehensively outlines the concrete, accessible pathways for applied researchers to deploy these advanced statistical techniques in real-world research scenarios. Specifically, the open-source statistical software JASP seamlessly executes the entire analytical pipeline, which provides an intuitive and user-friendly graphical user interface (GUI) for point-and-click execution. For researchers who require scriptability and reproducibility, specialized open-source packages make the methodology fully available into the R programming language. These programming tools facilitate automated reporting and extensive sensitivity analyses. They effectively lower the technical barriers to advanced Bayesian inference for non-statisticians. This paper effectively bridges the historical divide between intricate Bayesian theory and practical application. It delivers a definitive roadmap for researchers to maximize transparency and credibility in meta-analytic conclusions. Therefore, this methodology offers broad applicability for enhancing the robustness of evidence synthesis across psychological science and various other disciplines.关键词
贝叶斯模型平均/元分析/模型不确定性/发表偏倚/稳健贝叶斯元分析Key words
bayesian model averaging/meta-analysis/model uncertainty/publication bias/robust bayesian meta-analysis引用本文复制引用
任子伟,刘铮,胡传鹏.基于贝叶斯模型平均的元分析：原理与实现[EB/OL].(2026-05-17)[2026-05-19].https://chinaxiv.org/abs/202605.00116.学科分类
自然科学研究方法/数学
评论