# The metafor Package

A Meta-Analysis Package for R

faq

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 faq [2019/05/05 08:54]Wolfgang Viechtbauer faq [2019/05/15 19:05]Wolfgang Viechtbauer Both sides previous revision Previous revision 2019/05/15 19:05 Wolfgang Viechtbauer 2019/05/05 16:29 Wolfgang Viechtbauer 2019/05/05 08:54 Wolfgang Viechtbauer 2019/05/05 08:43 Wolfgang Viechtbauer 2019/03/05 11:28 Wolfgang Viechtbauer 2018/06/22 17:22 Wolfgang Viechtbauer 2018/06/22 17:22 Wolfgang Viechtbauer 2018/06/22 17:20 Wolfgang Viechtbauer [General Questions] 2018/06/22 17:11 Wolfgang Viechtbauer 2018/06/22 16:23 Wolfgang Viechtbauer 2016/06/07 19:34 Wolfgang Viechtbauer 2016/06/07 19:33 Wolfgang Viechtbauer 2015/12/08 14:01 Wolfgang Viechtbauer 2015/11/22 22:20 Wolfgang Viechtbauer 2015/05/05 12:00 Wolfgang Viechtbauer 2015/03/17 08:01 Wolfgang Viechtbauer 2015/01/31 18:59 Wolfgang Viechtbauer 2014/11/15 11:47 Wolfgang Viechtbauer 2014/09/25 16:28 Wolfgang Viechtbauer [Technical Questions] 2014/09/08 15:02 Wolfgang Viechtbauer 2014/08/17 11:36 Wolfgang Viechtbauer 2014/08/17 11:32 Wolfgang Viechtbauer [References] 2014/08/15 13:31 Wolfgang Viechtbauer [Technical Questions] 2014/08/10 13:30 Wolfgang Viechtbauer 2014/05/26 13:22 Wolfgang Viechtbauer [General Questions] 2014/05/21 13:53 Wolfgang Viechtbauer 2014/05/05 22:02 Wolfgang Viechtbauer 2014/05/05 14:04 Wolfgang Viechtbauer Next revision Previous revision 2019/05/15 19:05 Wolfgang Viechtbauer 2019/05/05 16:29 Wolfgang Viechtbauer 2019/05/05 08:54 Wolfgang Viechtbauer 2019/05/05 08:43 Wolfgang Viechtbauer 2019/03/05 11:28 Wolfgang Viechtbauer 2018/06/22 17:22 Wolfgang Viechtbauer 2018/06/22 17:22 Wolfgang Viechtbauer 2018/06/22 17:20 Wolfgang Viechtbauer [General Questions] 2018/06/22 17:11 Wolfgang Viechtbauer 2018/06/22 16:23 Wolfgang Viechtbauer 2016/06/07 19:34 Wolfgang Viechtbauer 2016/06/07 19:33 Wolfgang Viechtbauer 2015/12/08 14:01 Wolfgang Viechtbauer 2015/11/22 22:20 Wolfgang Viechtbauer 2015/05/05 12:00 Wolfgang Viechtbauer 2015/03/17 08:01 Wolfgang Viechtbauer 2015/01/31 18:59 Wolfgang Viechtbauer 2014/11/15 11:47 Wolfgang Viechtbauer 2014/09/25 16:28 Wolfgang Viechtbauer [Technical Questions] 2014/09/08 15:02 Wolfgang Viechtbauer 2014/08/17 11:36 Wolfgang Viechtbauer 2014/08/17 11:32 Wolfgang Viechtbauer [References] 2014/08/15 13:31 Wolfgang Viechtbauer [Technical Questions] 2014/08/10 13:30 Wolfgang Viechtbauer 2014/05/26 13:22 Wolfgang Viechtbauer [General Questions] 2014/05/21 13:53 Wolfgang Viechtbauer 2014/05/05 22:02 Wolfgang Viechtbauer 2014/05/05 14:04 Wolfgang Viechtbauer 2014/03/31 07:51 Wolfgang Viechtbauer [Technical Questions] 2013/12/20 18:50 Wolfgang Viechtbauer [Technical Questions] 2013/11/22 14:54 Wolfgang Viechtbauer 2013/11/22 14:51 Wolfgang Viechtbauer 2013/10/22 12:30 Wolfgang Viechtbauer [Technical Questions] 2013/10/22 08:08 Wolfgang Viechtbauer [Technical Questions] 2013/10/22 08:02 Wolfgang Viechtbauer 2013/07/15 11:05 Wolfgang Viechtbauer 2013/07/10 11:47 Wolfgang Viechtbauer 2013/07/10 11:37 Wolfgang Viechtbauer 2013/07/10 11:29 Wolfgang Viechtbauer 2013/07/10 10:28 Wolfgang Viechtbauer 2013/07/10 10:26 Wolfgang Viechtbauer 2013/07/10 10:23 Wolfgang Viechtbauer 2013/07/02 11:45 Wolfgang Viechtbauer 2013/06/26 22:58 Wolfgang Viechtbauer 2013/06/03 13:01 Wolfgang Viechtbauer 2013/06/03 12:42 Wolfgang Viechtbauer 2013/06/03 12:38 Wolfgang Viechtbauer 2013/06/03 12:36 Wolfgang Viechtbauer created Line 39: Line 39: ??? Is the package development funded? ??? Is the package development funded? - !!! For the most part, the development of the package has been funded through my own precious time. Through some collaborative work on the 'Open Meta-Analyst'​ software from the //Center for Evidence-Based Medicine// at Brown University, I have received some funding as part of a subcontract on a grant (thanks!). Also, Sandra Wilson and Mark Lipsey of the //Peabody Research Institute// at Vanderbilt University have provided funding that gave me some time and incentive for making the ''​rma.mv()''​ more efficient and for adding multicore capabilities to the ''​profile.rma.mv()''​ function. In this context, I also would like to mention Jason Hoeksema from the Department of Biology at the University of Mississippi,​ who invited me to be part of a working group at the //National Evolutionary Synthesis Center//, which gave me time over the course of several meetings to really develop the capabilities of the ''​rma.mv()''​ function. This collaboration also helped me better appreciate how important it is to listen to the users' needs when prioritizing additions to the package. However, further developments of the package could proceed much quicker if additional funding was available. If you are aware of any funding possibilities,​ feel free to let me know! + !!! For the most part, the development of the package has been funded through my own precious time. Through some collaborative work on the 'Open Meta-Analyst'​ software from the //Center for Evidence-Based Medicine// at Brown University, I have received some funding as part of a subcontract on a grant. Also, Sandra Wilson and Mark Lipsey of the //Peabody Research Institute// at Vanderbilt University have provided funding that gave me some time and incentive for making the ''​rma.mv()''​ more efficient and for adding multicore capabilities to the ''​profile.rma.mv()''​ function. In this context, I also would like to mention Jason Hoeksema from the Department of Biology at the University of Mississippi,​ who invited me to be part of a working group at the //National Evolutionary Synthesis Center//, which gave me time over the course of several meetings to really develop the capabilities of the ''​rma.mv()''​ function. This collaboration also helped me better appreciate how important it is to listen to the users' needs when prioritizing additions to the package. However, further developments of the package could proceed much quicker if additional funding was available. If you are aware of any funding possibilities,​ feel free to let me know! ??? How do I cite the package? ??? How do I cite the package? Line 63: Line 63: ??? How are $I^2$ and $H^2$ computed in the metafor package? ??? How are $I^2$ and $H^2$ computed in the metafor package? - !!! For random-effects models, the $I^2$ statistic is computed with $$I^2 = 100\% \times \frac{\hat{\tau}^2}{\hat{\tau}^2 + s^2},$$ where $\hat{\tau}^2$ is the estimated value of $\tau^2$ and $$s^2 = \frac{(k-1) \sum w_i}{(\sum w_i)^2 - \sum w_i^2},$$ where $w_i$ is the inverse of the sampling variance of the $i$th study ($s^2$ is equation 9 in Higgins & Thompson, 2002, and can be regarded as the '​typical'​ within-study variance of the observed effect sizes or outcomes). The $H^2$ statistic is computed with $$H^2 = \frac{\hat{\tau}^2 + s^2}{s^2}.$$ Analogous equations are used for mixed-effects models. + !!! For random-effects models, the $I^2$ statistic is computed with $$I^2 = 100\% \times \frac{\hat{\tau}^2}{\hat{\tau}^2 + \tilde{v}},$$ where $\hat{\tau}^2$ is the estimated value of $\tau^2$ and $$\tilde{v} ​= \frac{(k-1) \sum w_i}{(\sum w_i)^2 - \sum w_i^2},$$ where $w_i$ is the inverse of the sampling variance of the $i$th study ($\tilde{v}$ is equation 9 in Higgins & Thompson, 2002, and can be regarded as the '​typical'​ within-study variance of the observed effect sizes or outcomes). The $H^2$ statistic is computed with $$H^2 = \frac{\hat{\tau}^2 + \tilde{v}}{\tilde{v}}.$$ Analogous equations are used for mixed-effects models. Therefore, depending on the estimator of $\tau^2$ used, the values of $I^2$ and $H^2$ will change. For random-effects models, $I^2$ and $H^2$ are often computed in practice with $I^2 = 100\% \times (Q-(k-1))/​Q$ and $H^2 = Q/(k-1)$, where $Q$ denotes the statistic for the test of heterogeneity and $k$ the number of studies (i.e., observed effects or outcomes) included in the meta-analysis. The equations used in the metafor package to compute these statistics are based on more general definitions and have the advantage that the values of $I^2$ and $H^2$ will be consistent with the estimated value of $\tau^2$ (i.e., if $\hat{\tau}^2 = 0$, then $I^2 = 0$ and $H^2 = 1$ and if $\hat{\tau}^2 > 0$, then $I^2 > 0$ and $H^2 > 1$). Therefore, depending on the estimator of $\tau^2$ used, the values of $I^2$ and $H^2$ will change. For random-effects models, $I^2$ and $H^2$ are often computed in practice with $I^2 = 100\% \times (Q-(k-1))/​Q$ and $H^2 = Q/(k-1)$, where $Q$ denotes the statistic for the test of heterogeneity and $k$ the number of studies (i.e., observed effects or outcomes) included in the meta-analysis. The equations used in the metafor package to compute these statistics are based on more general definitions and have the advantage that the values of $I^2$ and $H^2$ will be consistent with the estimated value of $\tau^2$ (i.e., if $\hat{\tau}^2 = 0$, then $I^2 = 0$ and $H^2 = 1$ and if $\hat{\tau}^2 > 0$, then $I^2 > 0$ and $H^2 > 1$).