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

[Viechtbauer, Wolfgang (SP)]

The 48.97833 and 92.06504 are pseudo R^2 statistics, so they tell you that 49% of the between-study and 92% of the within-study heterogeneity are accounted for by the moderators. To me, that's more informative than saying something about how much of the unaccounted for variance is due to (the sum of) between- and within-study heterogeneity.

Best,
Wolfgang

>-----Original Message-----
>From: Ivan Jukic [mailto:ivan.jukic using aut.ac.nz]
>Sent: Wednesday, 13 October, 2021 4:32
>To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis using r-project.org
>Subject: Re: I2 interpretation for Multilevel meta-analysis with moderators
>
>Dear Wolfgang,
>
>thank you for explaining this and providing an example - I really appreciate it.
>
>Indeed, in the posts I linked, you made it clear that I2 meaning is not very
>intuitive (or even meaningful) in models with moderators. However, I would like
>to use it because these moderators are the most important thing in my analysis. I
>was thinking about just looking at I2 without moderators but these analyses are
>less meaningful for the story that I'm trying to tell. I'm now considering
>reporting both.
>
>I get (77.747826 3.745411 18.506763) for res0 (i.e., model without moderators),
>and (67.8411969 0.5082705 31.6505327) for res1 (i.e., model with moderators).
>
>After reading your response I'm now unsure what the numbers obtained by 100 *
>pmax(0, (res0$sigma2 - res1$sigma2) / res0$sigma2) actually mean? I get (48.97833
>92.06504).
>
>In your response, you interpreted this as "how much of the between-study and
>within-study heterogeneity is accounted for by the moderators". Based on these
>numbers, it seems like a lot of between- and within-study heterogenity is
>accounted for by the moderators. However, I can't interpret this in the same way
>by just looking at I2 for res0 and res1 (81.49% and 68.35%, respectively, OR even
>individual heterogeneity components from each model)? I guess I'm still missing
>something here.
>
>Cheers,
>Ivan