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analyses:raudenbush2009 [2018/12/08 12:57]
Wolfgang Viechtbauer
analyses:raudenbush2009 [2019/05/15 19:14] (current)
Wolfgang Viechtbauer
Line 103: Line 103:
 ==== Measures of Heterogeneity ==== ==== Measures of Heterogeneity ====
  
-As additional measures of heterogeneity,​ Raudenbush (2009) describes the "​variation to signal ratio" $H$ (p. 302) and the "​intra-class correlation"​ $\hat{\lambda}$ (p. 3030). First, note that $H$ is actually $H^2$ in the notation of Higgins and Thompson (2002) and $\hat{\lambda}$ is akin to $I^2$ (but not quite the same in the way it is computed). Moreover, note that $I^2$ and $H^2$ are computed in the metafor package based on more general definitions than typically used in practice. The equations used in the metafor package are described in detail under the [[:​faq#​technical_questions|frequently asked questions]] section. Depending on the method used to estimate $\tau^2$, one will get different values for $I^2$ and $H^2$. The equations that are typically used to compute $I^2$ and $H^2$ (i.e., $I^2 = 100\% \times (Q - (k-1))/Q$ and $H^2 = Q/(k-1)$) are actually special versions of the more general definitions used in the metafor package. When using the DerSimonian-Laird estimator of $\tau^2$, then the two definitions coincide. This can be seen if we use:+As additional measures of heterogeneity,​ Raudenbush (2009) describes the "​variation to signal ratio" $H$ (p. 302) and the "​intra-class correlation"​ $\hat{\lambda}$ (p. 3030). First, note that $H$ is actually $H^2$ in the notation of Higgins and Thompson (2002) and $\hat{\lambda}$ is akin to $I^2$ (but not quite the same in the way it is computed). Moreover, note that $I^2$ and $H^2$ are computed in the metafor package based on more general definitions than typically used in practice. The equations used in the metafor package are described in detail under the [[:​faq#​technical_questions|Frequently Asked Questions]] section. Depending on the method used to estimate $\tau^2$, one will get different values for $I^2$ and $H^2$. The equations that are typically used to compute $I^2$ and $H^2$ (i.e., $I^2 = 100\% \times (Q - (k-1))/Q$ and $H^2 = Q/(k-1)$) are actually special versions of the more general definitions used in the metafor package. When using the DerSimonian-Laird estimator of $\tau^2$, then the two definitions coincide. This can be seen if we use:
 <code rsplus> <code rsplus>
 res.DL <- rma(yi, vi, data=dat, digits=3, method="​DL"​) res.DL <- rma(yi, vi, data=dat, digits=3, method="​DL"​)
analyses/raudenbush2009.txt ยท Last modified: 2019/05/15 19:14 by Wolfgang Viechtbauer