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An alternative to R-2 for assessing linear models of effect size
Journal article   Open access   Peer reviewed

An alternative to R-2 for assessing linear models of effect size

Ariel M. Aloe, Betsy Jane Becker and Therese D. Pigott
Research synthesis methods, Vol.1(3-4), pp.272-283
07/01/2010
DOI: 10.1002/jrsm.23
PMID: 26061471
url
https://doi.org/10.1002/jrsm.23View
Published (Version of record) Open Access

Abstract

Reviewers often use regression models in meta-analysis ('meta-regressions') to examine the relationships between effect sizes and study characteristics. In this paper, we propose and illustrate the use of an index (R-Meta(2)) that expresses the amount of variance in the outcome that is explained by the meta-regression model. The values of R-2 obtained from the standard computer output for linear models of effect size in the meta-analysis context are typically too small, because the typical R-2 considers sampling variance to be unexplained whereas in meta-analysis it can be quantified. Although the idea of removing the unexplainable variance from the estimator of variance accounted for in meta-analysis is not new (Cook et al., 1992; Raudenbush, 1994) we explicitly define four estimators of variance explained, and illustrate via two examples that the typical R-2 obtained in a linear model of effect size is always lower than our indices. Thus, the typical R-2 underestimates the explanatory power of linear models of effect sizes. Our four estimators improve upon typical weighted R-2 values. Copyright (C) 2011 John Wiley & Sons, Ltd.
 Life Sciences & Biomedicine Mathematical & Computational Biology Multidisciplinary Sciences Science & Technology Science & Technology - Other Topics

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