[R-meta] Question Re: Rma.mv Model

[Tori Peña]

This is incredibly helpful!

I did not have specific sensitivity analyses in mind.  I'm open to any
suggestions based on your expertise.

On Wed, Sep 23, 2026 at 11:17 AM Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

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> Dear Tori,
>
> Please see my responses below.
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org>
> On Behalf
> > Of Tori Peña via R-sig-meta-analysis
> > Sent: Wednesday, September 23, 2026 16:38
> > To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-
> > project.org>
> > Cc: Tori Peña <Tori.Pena using stonybrook.edu>
> > Subject: [R-meta] Question Re: Rma.mv Model
> >
> > Hello everyone -
> >
> > I have a couple of questions related to a three-level model we plan to
> > conduct using *metafor. *For context, we have compiled correlations
> > indexing relationships between cognition and inflammation in the body. We
> > plan to nest effect sizes (level 1) in sample cohorts (level 2) within
> > studies (level 3). I wanted to check the following questions:
> >
> >    1. The literature has different types of correlations. Is it
> acceptable
> >    to convert all of these correlations to Fisher's *z *for the models?
> >    Or, should there way to handle these varying effect size types?
>
> You can use the standard r-to-z transformation on all kinds of correlation
> coefficients. However, the sampling variance equation 1/(n-3) only applies
> when converting Pearson product-moment correlations with the r-to-z
> transformation. For other types of correlation coefficients (Spearman,
> (point-)biserial, tetrachoric, (semi)partial, and so on), it would not be
> correct to use 1/(n-3) as the variance.
>
> Using the delta method, one can compute the variance of any r-to-z
> transformed correlation coefficient as long as one has an estimate of the
> variance of the correlation coefficient to begin with. For example, say you
> have a study that dichotomized both variables of interest and reports the
> results in terms of a 2x2 table (how many people scored above/below the
> cutoff on the first variable versus the second variable). Say this is the
> 2x2 table:
>
>        Above  Below
> Above  15     5
> Below   8     18
>
> Then we can get the tetrachoric correlation with:
>
> dat <- escalc(measure="RTET", ai=15, bi=5, ci=8, di=18)
> dat
>
>       yi     vi
> 1 0.6397 0.0258
>
> (this estimates the correlation between the underlying continuous
> variables). I can now r-to-z transform this with:
>
> transf.rtoz(dat$yi)
> [1] 0.757601
>
> But
>
> 1/((15+5+8+18)-3)
> [1] 0.02325581
>
> is NOT the sampling variance of the transformed tetrachoric correlation.
> Using the delta method, we can compute a correct (i.e., consistent)
> estimate of the sampling variance:
>
> conv.delta(yi, vi, data=dat, transf=transf.rtoz,
> replace=TRUE)
>
>       yi     vi
> 1 0.7576 0.0740
>
> Note that the variance (0.0740) is more than 3 times larger than the
> incorrect estimate (0.0233), because we lost information from the
> dichotomization of the two variables and having to reconstruct the
> correlation from that information. You can actually skip the whole
> conv.delta() thing since escalc() can directly do all of this for you:
>
> dat <- escalc(measure="ZTET", ai=15, bi=5, ci=8,
> di=18)
> dat
>
>
>
>       yi     vi
> 1 0.7576 0.0740
>
> The same principle applies to other correlation coefficients. Note that
> the r-to-z transformation is only a variance stabilizing transformation for
> Pearson product-moment correlations, not for (most) other types of
> correlation coefficients. However, using the transformation can still be
> advantageous, since raw correlations are bounded which can result in skewed
> sampling distributions. The r-to-z transformation can then help to
> normalize the sampling distributions.
>
> >    2. I could not find information in the *metafor *documentation about
> >    conducting sensitivity analyses for rma.mv objects. Is this
> possible? If
> >    so, how?
>
> What type of sensitivity analyses are you thinking of?
>
> > Thanks in advance,
> > Tori
> >
> > --
> > *Tori Peña, Ph.D. *(she/her/ella)
> > Lecturer of Psychology
> > Director, FaM Lab <
> https://protect.checkpoint.com/v2/r01/___https://ptori.github.io/famlab/___.YzJ1OnN0b255YnJvb2s6YzpnOmYxM2E4YzhiNjY2MjliNTU4ZTE2NmJjOTQwNGExMTk0Ojc6NWI5ZTpjNjZkOGU1N2Y1YTg2YzFkMDhkNTA4YzlhYTZhMGRhNGYwY2E4MjBjYmEzMTI2MWJlMTZmOGFiMDc5YzllNTMyOnA6VDpG
> >
> > Department of Psychology
> > Stony Brook University
> > [image: Stony Brook University logo]
>

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