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Cited by 205Meta-analysis and systematic reviewsStatistical Methods and Bayesian InferenceAdvanced Causal Inference Techniques

Neither fixed nor random: weighted least squares meta‐regression

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Stanley, T. D., Doucouliagos, Hristos·2017·Research Synthesis Methods
DOI 10.1002/jrsm.1211
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Abstract

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.

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  • Simulations show that there is little difference between random effects models and the UWLS-MRA, which appears to be even superior when there is a sizeable.

    “However, the simulations reported by Stanley & Doucouliagos, 2017) show that there is little difference between random effects models and the UWLS‐MRA, which appears to be even superior when there is a sizeable.”

    From Public sector reforms and their impact on the level of corruption: A systematic review (2021) · cites this paper as Stanley & Doucouliagos, 2017

  • Conventional meta-analytic models assume that sampling variances are known, whereas UWLS-MRA assumes they are known only up to a proportionality constant.

    “Conventional meta‐analytic models assume that the sampling variances are known. Conversely, the UWLS‐MRA assumes that the sampling variances are known only up to a proportionality constant σe2, which is “automatically estimated by the mean squared error, MSE” (Stanley & Doucouliagos, 2017, p. 22).”

    From Public sector reforms and their impact on the level of corruption: A systematic review (2021) · cites this paper as Stanley & Doucouliagos, 2017

  • Stanley & Doucouliagos (2017) proposed the Unconditional Weighted Least Square Meta-Regression Analysis (UWLS-MRA) as a third alternative to conventional meta-regression models.

    “Recently, Stanley & Doucouliagos, 2017) challenged the conventional meta (regression) models by proposing a third alternative: the Unconditional Weighted Least Square Meta‐Regression Analysis (henceforth UWLS‐MRA).”

    From Public sector reforms and their impact on the level of corruption: A systematic review (2021) · cites this paper as Stanley & Doucouliagos, 2017

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Authors
Stanley, T. D., & Doucouliagos, H.
Affiliations
  • Hendrix College (US)
  • Deakin University (AU)
Corresponding author
Stanley, T. D.
ORCID
Venue
Research Synthesis Methods
Publisher
Wiley
Published
2016-06-20
Volume
8
Issue
1
Pages
19-42
ISSN
  • 1759-2879 (ISSN-L)
  • 1759-2887
DOI
10.1002/jrsm.1211
OpenAlex
W2462813397
Cited by
205
References
67
Citations by year
2026: 7 · 2025: 17 · 2024: 17 · 2023: 28 · 2022: 24 · 2021: 31 · 2020: 26 · 2019: 23 · 2018: 15 · 2017: 13 · 2016: 2 · 2015: 1 · 2014: 1
FWCI
16.50
Type
journal article
Language
en
Open access
Licence
Locations
  • Research Synthesis Methods (publishedVersion)
  • PubMed (publishedVersion)
  • Figshare (submittedVersion, cc-by)
  • Zenodo (CERN European Organization for Nuclear Research) (submittedVersion, other-oa)
Funders
Grantová Agentura České Republiky (15‐02411S)
Topics
  • Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Keywords
publication bias, small sample bias, standard error correction, heterogeneity
MeSH terms
Algorithms, Computer Simulation, Humans, Markov Chains, Publishing, Regression Analysis, Research Design, Models, Statistical, Least-Squares Analysis, Publication Bias, Sample Size

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