元回归中效应量的最小个数需求：基于统计功效和估计精度

doi:10.3724/SP.J.1042.2020.00673

摘要/Abstract

摘要：

元回归模型被广泛应用于调节变量的识别。从元分析技术的原理谈起, 介绍了元回归模型, 然后采用蒙特卡洛模拟, 基于统计功效和估计精度探究效应量个数对元回归模型参数估计的影响, 从而确立效应量的最小个数需求。主要研究结果为：(1) Wald-type z检验方法在元回归中易犯I类错误; (2)为达到参数估计要求, 元回归至少需要20个效应量; (3)纳入合适的调节变量能降低对效应量的个数需求。基于研究结果, 提出以下建议：(1)研究者应慎重使用Wald-type z检验方法和CMA软件; (2)研究者至少需要20个效应量, 且应当根据实际情况进一步增加效应量个数; (3)研究者应当积极探索合适的调节变量; (4)未来审稿人可参考最小效应量个数需求对元回归研究进行质量评估。

关键词: 元分析, 元回归, 效应量, 最小个数需求

Abstract:

Meta-regression is the most frequently used technique for identifying moderators in meta-analysis. In this study, main principles and basic models of meta-analysis and meta-regression were briefly introduced first. Then a Monte Carlo simulation was conducted to investigate the minimum number of the effect size required in meta-regression based on statistical power and estimation precision. The results showed that (1) the Wald-type z test was prone to type I error in meta-regression; (2) at least 20 effect sizes were needed to meet parameter estimation requirements; (3) and inclusion of proper moderators could reduce the number of effect size required. Therefore, it is suggested that (1) meta-analysts should be careful when using the CMA software and the Wald-type z test; (2) at least 20 or more effect sizes are generally needed based on different situations; (3) exploration of moderators is necessary; (4) reviewers can value a meta-analysis research according to the minimum number of effect size required.

Key words: meta-analysis, meta-regression, effect size, minimum number requirement

中图分类号:

B841

方俊燕, 张敏强. (2020). 元回归中效应量的最小个数需求：基于统计功效和估计精度. 心理科学进展 , 28(4), 673-680.

FANG Junyan, ZHANG Minqiang. (2020). What is the minimum number of effect sizes required in meta-regression? An estimation based on statistical power and estimation precision. Advances in Psychological Science, 28(4), 673-680.

图/表 15

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检验方法	τ²=0.32
	β为0		β(均)较小		β(均)较大		β一个较大, 一个较小
	β = 0	β = (0,0)	β = 0.2	β = (0.2,0.2)	β = 0.5	β = (0.5,0.5)	β = (0.2,0.5)
Knha-test	38	38	38	38	38	38	38
z-test	43	43	43	43	43	43	43

检验方法	τ²=0.32
	β为0		β(均)较小		β(均)较大		β一个较大, 一个较小
	β = 0	β = (0,0)	β = 0.2	β = (0.2,0.2)	β = 0.5	β = (0.5,0.5)	β = (0.2,0.5)
Knha-test	38	38	38	38	38	38	38
z-test	43	43	43	43	43	43	43

检验方法	τ² = 0.08					τ² = 0.32
	β(均)较小		β(均)较大		β一个较大一个较小	β(均)较小		β(均)较大		β一个较大一个较小
	β = 0.2	β = (0.2, 0.2)	β = 0.5	β = (0.5, 0.5)	β = (0.2, 0.5)	β = 0.2	β = (0.2, 0.2)	β = 0.5	β = (0.5, 0.5)	β = (0.2, 0.5)
Knha-test	30	30	√	√	20	70	70	20	20	50
z-test	38	38	√	√	30	80	80	20	20	52

检验方法	τ² = 0.08					τ² = 0.32
	β(均)较小		β(均)较大		β一个较大一个较小	β(均)较小		β(均)较大		β一个较大一个较小
	β = 0.2	β = (0.2, 0.2)	β = 0.5	β = (0.5, 0.5)	β = (0.2, 0.5)	β = 0.2	β = (0.2, 0.2)	β = 0.5	β = (0.5, 0.5)	β = (0.2, 0.5)
Knha-test	30	30	√	√	20	70	70	20	20	50
z-test	38	38	√	√	30	80	80	20	20	52

回归系数取值	剩余异质性较小		剩余异质性较大
回归系数取值	包含一个调节变量	包含两个调节变量	包含一个调节变量	包含两个调节变量
β(均)为0	20	20	38	38
β(均)较小	30	30	70	70
β(均)较大	20	20	38	38
β₁较小β₂较大	——	20	——	50