[R-meta] I2 interpretation for Multilevel meta-analysis with moderators

Tue, Oct 12, 2021 6:30 AM

Hi Ivan,

I would say forget about I^2 in models with moderators. Nobody gets the meaning of this anyway :)

But in some way, one could interpret the 68.35% as indicating that 68.35% of the remaining variance (that is not accounted for already by the moderators) is due to the sum of study and effect size level heterogeneity (and the remaining 31.65% is due to sampling variance). I find this not particularly useful information.

Personally, as reader, I would want to know:

- for the model without moderators (say res0), the size of the variance components and whether the heterogeneity in the underlying true effects is more due to between-study or within-study heterogeneity; in essence:

res0$sigma2
100 * res0$sigma2 / sum(res0$sigma2)

- one could also report the I^2 values for between-study heterogeneity, within-study heterogeneity, and sampling variance; in essence:

k <- res0$k
wi <- 1/res0$vi
vt <- (k-1) * sum(wi) / (sum(wi)^2 - sum(wi^2))
100 * c(res0$sigma2, vt) / (sum(res0$sigma2) + vt)

- and for the model involving moderators (say res1), how much of the between-study and within-study heterogeneity is accounted for by the moderators; in essence:

100 * pmax(0, (res0$sigma2 - res1$sigma2) / res0$sigma2)

(note: pmax(0, ...) since these pseudo R^2 values can be negative)

So, no I^2 type values based on res1.

Best,
Wolfgang

[R-meta] I2 interpretation for Multilevel meta-analysis with moderators

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