faq

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faq [2019/05/05 16:29] Wolfgang Viechtbauer |
faq [2019/05/15 19:05] Wolfgang Viechtbauer |
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??? 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 $H^2 > 1$). |

faq.txt ยท Last modified: 2019/05/15 19:05 by Wolfgang Viechtbauer

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