Neither fixed nor random: weighted least squares meta‐regression

• Published in: Research synthesis methods Vol. 8; no. 1; pp. 19 - 42
• Main Authors: Stanley, T. D., Doucouliagos, Hristos
• Format: Journal Article
• Language: English
• Published: England Wiley-Blackwell 01.03.2017; Wiley Subscription Services, Inc
• Subjects: Algorithms; Bias; Computer Simulation; Error Correction; fixed effect; Humans; Least Squares Statistics; Least-Squares Analysis; Markov Chains; Medical Research; Meta Analysis; meta‐regression; Models, Statistical; Publication Bias; Publishing; random effects; Regression (Statistics); Regression Analysis; Research Design; Research methodology; Research Reports; Sample Size; Simulation; Statistical Significance; weighted least squares; random effects; fixed effect; weighted least squares; meta-regression
• ISSN: 1759-2879; 1759-2887
• DOI: 10.1002/jrsm.1211

Our study revisits and challenges two core conventional meta‐regression estimators: the prevalent use of ‘mixed‐effects’ or random‐effects meta‐regression analysis and the correction of standard errors that defines fixed‐effects meta‐regression analysis (FE‐MRA). We show how and explain why an unrestricted weighted least squares MRA (WLS‐MRA) estimator is superior to conventional random‐effects (or mixed‐effects) meta‐regression when there is publication (or small‐sample) bias that is as good as FE‐MRA in all cases and better than fixed effects in most practical applications. Simulations and statistical theory show that WLS‐MRA provides satisfactory estimates of meta‐regression coefficients that are practically equivalent to mixed effects or random effects when there is no publication bias. When there is publication selection bias, WLS‐MRA always has smaller bias than mixed effects or random effects. In practical applications, an unrestricted WLS meta‐regression is likely to give practically equivalent or superior estimates to fixed‐effects, random‐effects, and mixed‐effects meta‐regression approaches. However, random‐effects meta‐regression remains viable and perhaps somewhat preferable if selection for statistical significance (publication bias) can be ruled out and when random, additive normal heterogeneity is known to directly affect the ‘true’ regression coefficient. Copyright © 2016 John Wiley & Sons, Ltd.