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--- analyses:berkey1998 [2023/06/01 12:30] – Wolfgang Viechtbauer
+++ analyses:berkey1998 [2023/06/22 11:42] (current) – Wolfgang Viechtbauer
@@ Line 58: / Line 58: @@
 A multivariate random-effects model can now be used to meta-analyze the two outcomes simultaneously. The model is given by $$\left[ \begin{array}{c}
-   y_{AL,i}\\
+   y_{PD,i}\\
-   y_{PD,i}
+   y_{AL,i}
 \end{array} \right]
    =
 \left[ \begin{array}{c}
-   \mu_{AL} \\
+   \mu_{PD} \\
-   \mu_{PD}
+   \mu_{AL}
 \end{array} \right]
    +
 \left[ \begin{array}{c}
-   u_{AL,i} \\
+   u_{PD,i} \\
-   u_{PD,i}
+   u_{AL,i}
 \end{array} \right]
    +
 \left[ \begin{array}{c}
-   \epsilon_{AL,i} \\
+   \epsilon_{PD,i} \\
-   \epsilon_{PD,i}
+   \epsilon_{AL,i}
-\end{array} \right],$$ where $$\mbox{Var}
+\end{array} \right],$$ where $$G = \mbox{Var}
 \left[ \begin{array}{c}
-   u_{AL,i} \\
+   u_{PD,i} \\
-   u_{PD,i}
+   u_{AL,i}
 \end{array} \right]
    =
 \left[ \begin{array}{cc}
-   \tau^2_{AL}              & \rho \tau_{AL} \tau_{PD} \\
+   \tau^2_{PD}              & \rho \tau_{PD} \tau_{AL} \\
-   \rho \tau_{AL} \tau_{PD} & \tau^2_{PD}
+   \rho \tau_{PD} \tau_{AL} & \tau^2_{AL}
-\end{array} \right]$$ and $$\mbox{Var}
+\end{array} \right]$$ and $$V_i = \mbox{Var}
 \left[ \begin{array}{c}
-   \epsilon_{AL,i} \\
+   \epsilon_{PD,i} \\
-   \epsilon_{PD,i}
+   \epsilon_{AL,i}
 \end{array} \right]
    =
 \left[ \begin{array}{cc}
-   \mbox{var}_{AL,i}      & \mbox{cov}_{AL,i;PD,i} \\
+   \mbox{var}_{PD,i}      & \mbox{cov}_{PD,i;AL,i} \\
-   \mbox{cov}_{AL,i;PD,i} & \mbox{var}_{PD,i}
+   \mbox{cov}_{PD,i;AL,i} & \mbox{var}_{AL,i}
-\end{array} \right],$$ where the elements in this second variance-covariance matrix are given by the $2 \times 2$ blocks along the diagonal in the ''V'' matrix. We can fit this model with:
+\end{array} \right],$$ where the elements in this second variance-covariance matrix are given by the $2 \times 2$ blocks along the diagonal in the ''V'' matrix. Therefore, $$V = \left[ \begin{array}{ccc}
+   V_1 &        & \\
+       & \ddots & \\
+       &        & V_5
+\end{array} \right].$$
+We can fit this model with:
 <code rsplus>