[R-meta] Questions Re: I^2

[Tori Peña]

Hi again,

I just wanted to follow-up on this email -

I am running a three-level rma.mv model in R. When I calculated I^2, it
suggested that 78% of heterogeneity is *within *clusters in level two.  I
wasn't sure if this suggests that we should not conduct moderator analyses
or if it suggests we should consider a two-level model?  Thanks in advance
for your guidance!

See code below:

m_1 <- rma.mv(yi = yi,
                     V = vi,
                     slab = StudyID,
                     data = nestedAgg,
                     random = ~ 1 | StudyID/ESid,
                     test = "t",
                     method = "REML")

W <- diag(1/m_1$vi)
X <- model.matrix(m_1)
P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W
100 * sum(m_1$sigma2) / (sum(m_1$sigma2) + (m_1$k-m_1$p)/sum(diag(P)))

100 * m_1$sigma2 / (sum(m_1$sigma2) + (m_1$k-m_1$p)/sum(diag(P)))

[OUTPUT: ## [1] 9.890334 77.989904]

On Tue, Apr 15, 2025 at 11:20 AM Tori Peña <Tori.Pena using stonybrook.edu> wrote:

> Hi everyone,
>
> I am running a three-level rma.mv model in R. When I calculated I^2, it
> suggested that 78% of heterogeneity is *within *clusters in level two.  I
> wasn't sure if this suggests that we should not conduct moderator analyses
> or if it suggests we should consider a two-level model?  Thanks in advance
> for your guidance!
>
> See code below:
>
> m_1 <- rma.mv(yi = yi,
>                      V = vi,
>                      slab = StudyID,
>                      data = nestedAgg,
>                      random = ~ 1 | StudyID/ESid,
>                      test = "t",
>                      method = "REML")
>
> W <- diag(1/m_1$vi)
> X <- model.matrix(m_1)
> P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W
> 100 * sum(m_1$sigma2) / (sum(m_1$sigma2) + (m_1$k-m_1$p)/sum(diag(P)))
>
> 100 * m_1$sigma2 / (sum(m_1$sigma2) + (m_1$k-m_1$p)/sum(diag(P)))
>
> [OUTPUT: ## [1] 9.890334 77.989904]
>
> Thanks,
> Tori
>
> --
> *Tori Peña, Ph.D. *(she/her/ella)
> Cognitive Psychology
> Dept. of Psychology
> Stony Brook University
> Stony Brook, NY 11790-2500
> [image: Stony Brook University logo]
>

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