[R-meta] R-sig-meta-analysis Digest, Vol 89, Issue 13

[Viechtbauer, Wolfgang (NP)]

Hi Beate,

The simulations I mentioned are not published, but Fisher (1925) directly states this as well, so you can stick to that reference.

By the way, I just added a deltamethod() function to the development version of the metafor package. So, coming back to this model:

model <- rma.mv(
   zi,
   vzi,
   random = list(~ MZDZ_factor | Study_ID, ~ MZDZ_factor | ESID), struct="UN",
   data = data,
   mods = ~ 0 + MZDZ_factor,
   method = "REML",
   tdist = TRUE)

you can now just do:

deltamethod(model, fun=function(b1,b2) 2*(transf.ztor(b2) - transf.ztor(b1)))

and you will directly get the estimate of h^2 and the corresponding SE and CI.

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of St Pourcain, Beate via R-sig-meta-analysis
> Sent: Sunday, October 20, 2024 21:25
> To: r-sig-meta-analysis using r-project.org
> Cc: St Pourcain, Beate <Beate.StPourcain using mpi.nl>
> Subject: Re: [R-meta] R-sig-meta-analysis Digest, Vol 89, Issue 13
>
> Hi Michael,
>
> Thanks for pointing this out! The Fisher reference will certainly do. I had
> hoped to get the reference for "simulation studies I have done confirm this",
> but that's an added bonus.
>
> Have a nice evening,
> Beate
>
> Date: Sat, 19 Oct 2024 15:16:22 +0100
> From: Michael Dewey <lists using dewey.myzen.co.uk>
> To: R Special Interest Group for Meta-Analysis
>         <r-sig-meta-analysis using r-project.org>, "Viechtbauer, Wolfgang (NP)"
>         <wolfgang.viechtbauer using maastrichtuniversity.nl>
> Cc: "St Pourcain, Beate" <Beate.StPourcain using mpi.nl>
> Subject: Re: [R-meta] Meta-analysis of intra class correlation
>         coefficients
>
> Dear Beate
>
> Somewhere buried in this thread Wolfgang said
>
> ==========================
> This goes back to Fisher (1925; Statistical methods for research workers).
>
> In your application (where you dealing with pairs), n is the number of
> pairs and m is 2. In that case, you can treat ICC(1) values like regular
> correlations. However, if you do apply the r-to-z transformation, then
> Fisher suggests to use 1/(n-3/2) as the variance (instead of 1/(n-3) as
> we typically use for r-to-z transformed Pearson product-moment
> correlation coefficients) and simulation studies I have done confirm this.
> ======================
>
> Michael
>
> On 18/10/2024 19:43, St Pourcain, Beate via R-sig-meta-analysis wrote:
> > Dear Wolfgang,
> > No worries, I am aware of the difference and fully agree with your comments. I
> was just surprised by the similarity in estimates and had hoped for an
> approximation that  might provide a quick workaround in the current situation.
> Thanks again for all your help, we will take it from here.
> >
> > In case you would have (at some point) a reference for the variance of Z
> scores for ICCs as
> >
> > 1/( n-3/2)
> >
> > that would be great, no rush!
> >
> > Enjoy your weekend,
> > Beate