[R-meta] Effect size for F-test

[Viechtbauer, Wolfgang (SP)]

Dear Crystal,

Not sure what the reviewer wants. The coefficients for different levels of 'iv_category' are contrasts between these levels and the reference level of 'iv_category' and in that sense could be considered to be the 'effect sizes' but there is not just one such 'effect size' but as many as there are contrasts.

But I suspect that the reviewer, seeing an F-test, is asking about something like eta-squared (or R-squared). For this, you can do the following:

mod.iv <- rma.mv(yi, vi, data = meta, mods = ~ factor(iv_category),
                 random = list(~ 1 | id, ~ 1 | no_effects), tdist = TRUE)

mod.0 <- rma.mv(yi, vi, data = meta,
                 random = list(~ 1 | id, ~ 1 | no_effects), tdist = TRUE)

(mod.0$sigma2 - mod.iv$sigma2) / mod.0$sigma2

which gives the proportional reduction in the two variance components when iv_category is added as a moderator and these are pseudo R-squared type measures. If you just want a single R-squared value, then use

(sum(mod.0$sigma2) - sum(mod.iv$sigma2)) / sum(mod.0$sigma2)

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Crystal La Rue
>Sent: Tuesday, 15 June, 2021 12:17
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Effect size for F-test
>
>Dear Wolfgang,
>
>We conducted a three-level meta-analysis using metafor (specifically the rma.mv
>function). We also looked at "IV category" as a moderator using the code below. A
>reviewer has asked that we report the effect size for this F-test, but I'm not
>sure where to find this in the output. Is there a way to get this?
>
>mod.iv <- rma.mv(yi, vi, data = meta, mods = ~ factor(iv_category),
>                 random = list(~ 1 | id, ~ 1 | no_effects), tdist = TRUE)
>mod.iv
>
>Many thanks in advance for your help,
>Crystal
>
>Crystal La Rue
>
>PhD Candidate, Research Assistant
>
>School of Psychology,
>
>The University of Queensland
>
>St Lucia, QLD, 4072 Australia