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--- faq [2022/08/30 11:18] – Wolfgang Viechtbauer
+++ faq [2022/09/25 11:23] – Wolfgang Viechtbauer
@@ Line 73: / Line 73: @@
 ??? For mixed-effects models, how is the $R^2$ statistic computed by the rma() function?
-!!! The pseudo $R^2$ statistic (Raudenbush, 2009) is computed with $$R^2 = \frac{\hat{\tau}_{RE}^2 - \hat{\tau}_{ME}^2}{\hat{\tau}_{RE}^2},$$ where $\hat{\tau}_{RE}^2$ denotes the estimated value of $\tau^2$ based on the random-effects model (i.e., the total amount of heterogeneity) and $\hat{\tau}_{ME}^2$ denotes the estimated value of $\tau^2$ based on the mixed-effects model (i.e., the residual amount of heterogeneity). It can happen that $\hat{\tau}_{RE}^2 < \hat{\tau}_{ME}^2$, in which case $R^2$ is set to zero. Again, the value of $R^2$ will change depending on the estimator of $\tau^2$ used. Also note that this statistic is only computed when the mixed-effects model includes an intercept (so that the random-effects model is clearly nested within the mixed-effects model). You can also use the ''[[https://wviechtb.github.io/metafor/reference/anova.rma.html|anova()]]'' function to compute $R^2$ for any two models that are known to be nested.
+!!! The pseudo $R^2$ statistic (Raudenbush, 2009) is computed with $$R^2 = \frac{\hat{\tau}_{RE}^2 - \hat{\tau}_{ME}^2}{\hat{\tau}_{RE}^2} = 1 - \frac{\hat{\tau}_{ME}^2}{\hat{\tau}_{RE}^2},$$ where $\hat{\tau}_{RE}^2$ denotes the estimated value of $\tau^2$ based on the random-effects model (i.e., the total amount of heterogeneity) and $\hat{\tau}_{ME}^2$ denotes the estimated value of $\tau^2$ based on the mixed-effects model (i.e., the residual amount of heterogeneity). It can happen that $\hat{\tau}_{RE}^2 < \hat{\tau}_{ME}^2$, in which case $R^2$ is set to zero. Again, the value of $R^2$ will change depending on the estimator of $\tau^2$ used. Also note that this statistic is only computed when the mixed-effects model includes an intercept (so that the random-effects model is clearly nested within the mixed-effects model). You can also use the ''[[https://wviechtb.github.io/metafor/reference/anova.rma.html|anova()]]'' function to compute $R^2$ for any two models that are known to be nested.
 ??? For random-effects models fitted with the rma() function, how is the prediction interval computed by the predict() function?