tips:weights_in_rma.mv_models
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tips:weights_in_rma.mv_models [2021/11/08 15:16] – Wolfgang Viechtbauer | tips:weights_in_rma.mv_models [2021/11/08 15:56] – Wolfgang Viechtbauer | ||
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===== Weights in Models Fitted with the rma.mv() Function ===== | ===== Weights in Models Fitted with the rma.mv() Function ===== | ||
- | One of the fundamental concepts underlying a meta-analysis is the idea of weighting: More precise estimates are given more weight in the analysis then less precise estimates. In ' | + | One of the fundamental concepts underlying a meta-analysis is the idea of weighting: More precise estimates are given more weight in the analysis then less precise estimates. In ' |
==== Models Fitted with the rma() Function ==== | ==== Models Fitted with the rma() Function ==== | ||
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Variable '' | Variable '' | ||
- | We now fit fixed- and random-effects models to these estimates. | + | We now fit equal- and random-effects models to these estimates. |
<code rsplus> | <code rsplus> | ||
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{{ tips: | {{ tips: | ||
- | In the FE model, the weights given to the estimates are equal to $w_i = 1 / v_i$, where $v_i$ is the sampling variance of the $i$th study. This is called ' | + | In the equal-effects |
In the RE model, the estimates are weighted with $w_i = 1 / (\hat{\tau}^2 + v_i)$. Therefore, not only the sampling variance, but also the (estimated) amount of heterogeneity (i.e., the variance in the underlying true effects) is taken into consideration when determining the weights. When $\hat{\tau}^2$ is large (relative to the size of the sampling variances), then the weights actually become quite similar to each other. Hence, smaller (less precise) studies may receive almost as much as weight as larger (more precise) studies. We can in fact see this happening in the present example. While the three studies mentioned above still receive the largest weights, their weights are now much more similar to those of the other studies. As a result, the summary estimate is not as strongly pulled to the right by the TPT Madras study. | In the RE model, the estimates are weighted with $w_i = 1 / (\hat{\tau}^2 + v_i)$. Therefore, not only the sampling variance, but also the (estimated) amount of heterogeneity (i.e., the variance in the underlying true effects) is taken into consideration when determining the weights. When $\hat{\tau}^2$ is large (relative to the size of the sampling variances), then the weights actually become quite similar to each other. Hence, smaller (less precise) studies may receive almost as much as weight as larger (more precise) studies. We can in fact see this happening in the present example. While the three studies mentioned above still receive the largest weights, their weights are now much more similar to those of the other studies. As a result, the summary estimate is not as strongly pulled to the right by the TPT Madras study. |
tips/weights_in_rma.mv_models.txt · Last modified: 2023/08/03 13:37 by Wolfgang Viechtbauer