# Deriving heterogeneity measures for each level in a multi-level moderator meta-analysis

I'm running a multi-level moderator meta-analysis using the R package metafor. To derive $$I^2$$ for the metafor analysis as a whole, which doesn't come out automatically for multi-level models, I've used the formulas described here.

However, I've seen meta-analysis articles where heterogeneity measures, such as $$I^2$$, are reported for the individual levels in the moderator analysis.

How would these be computed? I realize that I could run subset analyses for each level, but could I somehow get the values directly from the moderator analysis? Does it even make sense to ask for heterogeneity measures for each of the levels in a moderator analysis?

• Does this stats.stackexchange.com/questions/187197/… help? – mdewey Nov 24 '18 at 12:43
• @mdewey Thanks, I've seen that question. It seem to be about how to get $I^2$ for the overall result. – Speldosa Nov 24 '18 at 14:57
• I think that if you run the example you get an $I^2$-like measure corresponding to each $\sigma^2$ – mdewey Nov 24 '18 at 15:28
• Also the first link you provided explains this. See the part: "However, we can also break things down to estimate how much of the total variance can be attributed to between- and within-cluster heterogeneity separately". – Wolfgang Nov 25 '18 at 19:57
• I think you are not fully appreciating how vectorisation works in R. WHy not just try the code and see what happens? Note that questions which are mostly code-related might be better on the mailing list stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis/ You do have to register first. – mdewey Nov 26 '18 at 11:47