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Better than Random: Weighted Least Squares Meta-Regression Analysis

  • T.D. Stanley


  • Hristos Doucouliagos


Our study revisits and challenges two core conventional meta-regression models: the prevalent use of ‘mixed-effects’ or random-effects meta-regression analysis (RE-MRA) and the correction of standard errors that defines fixed-effects meta-regression analysis (FE-MRA). We show how and explain why the traditional, unrestricted weighted least squares estimator (WLS-MRA) is superior to conventional random-effects (or mixed-effects) meta-regression when there is publication (or small-sample) bias and as good as FE-MRA in all cases and better in most practical applications. Simulations and statistical theory show that WLS-MRA provides satisfactory estimates of meta-regression coefficients with confidence intervals that are comparable to mixed-or random-effects when there is no publication bias. When there is publication selection bias, WLS-MRA dominates mixed- and random-effects, especially when there is large additive heterogeneity as assumed by the random-effects meta-regression model.

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Paper provided by Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance in its series Economics Series with number 2013_2.

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Date of creation: 17 Aug 2013
Date of revision:
Handle: RePEc:dkn:econwp:eco_2013_2
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  1. Hristos Doucouliagos & Janto Haman & T.D. Stanley, 2010. "Pay for Performance and Corporate Governance Reform," Economics Series 2010_04, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  2. T.D. Stanley & Stephen B. Jarrell & Hristos Doucouliagos, 2009. "Could It Be Better to Discard 90% of the Data? A Statistical Paradox," Economics Series 2009_13, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  3. Havranek, Tomas, 2009. "Rose Effect and the Euro: Is the Magic Gone?," MPRA Paper 18479, University Library of Munich, Germany, revised 07 Nov 2009.
  4. Christoph Engel, 2011. "Dictator games: a meta study," Experimental Economics, Springer, vol. 14(4), pages 583-610, November.
  5. Doucouliagos, Chris & Stanley, T.D. & Giles, Margaret, 2012. "Are estimates of the value of a statistical life exaggerated?," Journal of Health Economics, Elsevier, vol. 31(1), pages 197-206.
  6. T. D. Stanley, 2008. "Meta-Regression Methods for Detecting and Estimating Empirical Effects in the Presence of Publication Selection," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(1), pages 103-127, 02.
  7. John Copas & Claudia Lozada-Can, 2009. "The radial plot in meta-analysis: approximations and applications," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 329-344.
  8. Ian R. White, 2011. "Multivariate random-effects meta-regression: Updates to mvmeta," Stata Journal, StataCorp LP, vol. 11(2), pages 255-270, June.
  9. Stanley, T D & Jarrell, Stephen B, 1989. " Meta-Regression Analysis: A Quantitative Method of Literature Survey s," Journal of Economic Surveys, Wiley Blackwell, vol. 3(2), pages 161-70.
  10. Hristos Doucouliagos & T.D. Stanley, 2008. "Theory Competition and Selectivity: Are All Economic Facts Greatly Exaggerated?," Economics Series 2008_06, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  11. J. Barkley Rosser, 2009. "Introduction," Chapters, in: Handbook of Research on Complexity, chapter 1 Edward Elgar.
  12. Hristos Doucouliagos & T.D. Stanley, 2008. "Publication Selection Bias in Minimum-Wage Research? A Meta-Regression Analysis," Economics Series 2008_14, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  13. Maria Abreu Henri L. F. de Groot & Raymond J. G. M. Florax, 2005. "A Meta-Analysis of β-Convergence: the Legendary 2%," Journal of Economic Surveys, Wiley Blackwell, vol. 19(3), pages 389-420, 07.
  14. T.D. Stanley & Hristos Doucouliagos, 2011. "Meta-Regression Approximations to Reduce Publication Selection Bias," Economics Series 2011_4, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
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