I want to run a meta-analysis and I have to set up a weighted sample for each subsample from my study. For example a paper reports four different fiscal multipliers estimates (these are the observations from the paper) and I know that I have to include every estimate weighted 1/4. My question is how can I equally weight every study? How can I weight the rest of the sub-samples, like the type of econometric model, data length etc.? I have all the data in Excel and I don't know how to prepare all these variables for the meta regression. It's the first time when I perform such an analysis. Thank you in advance!
Typically in a fixed effect meta-analysis model, the effect size is weighted by the inverse of its associated variance. First, W(i) = 1/V(i); Weight of the i'th effect size = W, variance of the i'th effect size = V. Then sum the products of the weights, W(i), with their associated effect size, (E(i)), and divide by the sum of the weights; sum[W(i)*E(i)] / sum[W(i)].
Since you have multiple effect sizes per study and multiple studies, then a random model is probably more appropriate. I would not simply average effect sizes per study as you described in your example with the "1/4" weight. This is because not all studies are created equal. Starting with chapter 11 (fixed-effect meta) and 12 (random effect meta) from Borenstein et al.'s Intro to Meta-Analysis should get you off on the right track. Here is a PDF of the text online. https://www.meta-analysis-workshops.com/download/bookChapterSample.pdf
Good luck! I hope that helped.
I also agree with @Blake Carlton Jones regarding the recommended tutorial link to learn about weighting in meta analysis
@Blake Carlton Jones in the study that I've attached here (p. 14, second paragraph) is an example about the way of weighting sample. Unfortunately, I can't understand the process. I will appreciate if you take a look over this study.
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