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<p>Dear Wolfgang,</p>
<p>thank you so much, this works perfectly well for me!</p>
<p>I have one final questions before I'm ready to analyze my data:
Could I check whether this moderation by variable type is
moderated by study characteristics? I.e., is there a way to
include an interaction term that again specifically tests if
moderator M moderates the difference in correlations between X and
Y? I found your example on two categorial moderates and think I
could apply that, but most of the moderators I'm thinking about
are metric variables. <br>
</p>
<p>Best,</p>
<p>Anna-Lena<br>
</p>
<br>
<div class="moz-cite-prefix">Am 15.08.2018 um 14:50 schrieb
Viechtbauer, Wolfgang (SP):<br>
</div>
<blockquote type="cite"
cite="mid:d13e27d40be546b0b9bd1c228254a8be@UM-MAIL3214.unimaas.nl">
<pre wrap="">library(metafor)
source(<a class="moz-txt-link-rfc2396E" href="https://gist.githubusercontent.com/wviechtb/700983ab0bde94bed7c645fce770f8e9/raw/5bb5601852b132af533aef41405d58a3ae04cf82/rmat.r">"https://gist.githubusercontent.com/wviechtb/700983ab0bde94bed7c645fce770f8e9/raw/5bb5601852b132af533aef41405d58a3ae04cf82/rmat.r"</a>)
dat <- read.table(header=TRUE, text = "
study var1 var2 ri ni
1 X Y .20 50
1 X Z .30 50
1 Y Z .52 50
2 X Y .34 35
2 X Z .43 35
2 Y Z .44 35")
dat2 <- rmat(ri ~ var1 + var2 | study, n=c(50,35), data=dat)
dat2
res <- rma.mv(yi, dat2$V, mods = ~ var1var2 - 1, random = ~ var1var2 | id, struct="UN", data=dat2$dat)
res
### three contrasts
anova(res, L=c(1, -1, 0))
anova(res, L=c(1, 0, -1))
anova(res, L=c(0, 1, -1))
You are interested in the first of these three contrasts, that is, whether cor(X,Y) = cor(X,Z).
Actually, I would recommend to work with:
dat2 <- rmat(ri ~ var1 + var2 | study, n=c(50,35), data=dat, rtoz=TRUE)
dat2
This applies Fisher's r-to-z transformation.
Best,
Wolfgang
-----Original Message-----
From: Anna-Lena Schubert [<a class="moz-txt-link-freetext" href="mailto:anna-lena.schubert@psychologie.uni-heidelberg.de">mailto:anna-lena.schubert@psychologie.uni-heidelberg.de</a>]
Sent: Wednesday, 15 August, 2018 11:08
To: Viechtbauer, Wolfgang (SP); <a class="moz-txt-link-abbreviated" href="mailto:r-sig-meta-analysis@r-project.org">r-sig-meta-analysis@r-project.org</a>
Subject: Re: [R-meta] Comparing dependent, overlapping correlation coefficients
Hi Wolfgang,
thanks so much, I now believe I have sensible values in my V matrix.
They deviate slightly from manual calculations, but are really close.
I'm still lost on how to test for the interaction between X and Y then,
though. I tried
res <- rma.mv(yi, V, mods = ~ variable | studyID, data=dat,
method="ML"),
but the results don't correspond to the univariate meta-analyses I
conducted before. In addition, it tests (I believe) for a moderation of
all three correlations, while I'm only interested in the difference
between r_XY and r_XZ. Moreover, the manual says "In case the sampling
errors are correlated, then one can specify the entire
variance-covariance matrix of the sampling errors via the V argument",
but it seems I cannot simply leave "yi" out of the argument.
Best, Anna-Lena
Am 14.08.2018 um 22:18 schrieb Viechtbauer, Wolfgang (SP):
</pre>
<blockquote type="cite">
<pre wrap="">You do not need escalc(). The rmat() function gives you the variances along the diagonal of the 'V' matrix.
The variances should be (1 - ri^2)^2 / (ni - 1). You should be able to double-check that these values correspond to your data. Since ni should be the same for r_XY and r_XZ within a study, then it might be that the variances are roughly the same if the two correlations are not all that different. They should not be identical though (unless r_XY and r_XZ are the same).
Best,
Wolfgang
-----Original Message-----
From: R-sig-meta-analysis [<a class="moz-txt-link-freetext" href="mailto:r-sig-meta-analysis-bounces@r-project.org">mailto:r-sig-meta-analysis-bounces@r-project.org</a>] On Behalf Of Anna-Lena Schubert
Sent: Tuesday, 14 August, 2018 14:20
To: James Pustejovsky
Cc: <a class="moz-txt-link-abbreviated" href="mailto:r-sig-meta-analysis@r-project.org">r-sig-meta-analysis@r-project.org</a>
Subject: Re: [R-meta] Comparing dependent, overlapping correlation coefficients
Hi James,
I used Wolfgang's script on git to calculate the Cov(r_XY, r_XZ) by feeding it Cor(r_YZ). In the next step, I calculated Var(r_XY) and Var(r_XZ) by using the escalc function. However, Var(r_XY) always equals Var(r_XZ) for each study. Does this make sense?
I nevertheless added all three measures per study into a variance-covariance matrix such as:
r_XY r_XZ r_XY r_XZ
r_XY 0.004 0.0001 0 0
r_XZ 0.0001 0.004 0 0
r_XY 0 0 0.008 0.002
r_XZ 0 0 0.002 0.008
Then, I tried to feed everything into a multivariate meta-analysis:
res <- rma.mv(yi, V, mods = ~ variableType - 1, random = ~ variableType | studyNum, struct="UN", data=dat, method="ML")
The estimates I get for both of the correlation coefficients correspond closely to those I get when only meta-analyzing one of the variable types, which seems great. However, I'm still somewhat concerned that Var(r_XY) = Var(r_XZ). Do you think there may have been some mistake in my code or does it make sense that these variances are equal?
Best,
Anna-Lena
Am 10.08.2018 um 17:06 schrieb James Pustejovsky:
Anna-Lena,
The approach that you suggested (putting the data in "long" format and defining an indicator variable for whether Y or Z is the correlate) is just what I would recommend. However, there is a complication in that the estimates r_XY and r_XZ are correlated (correlated correlation coefficients...say that six times fast!), and the degree of correlation depends on r_YZ.
1) If you have extracted data on r_YZ then you could use this to compute Cov(r_XY, r_XZ) and then do a multivariate meta-analysis. See discussion here:
<a class="moz-txt-link-freetext" href="https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-January/000483.html">https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-January/000483.html</a>
And this function for computing the required covariance matrices:
<a class="moz-txt-link-freetext" href="https://gist.github.com/wviechtb/700983ab0bde94bed7c645fce770f8e9">https://gist.github.com/wviechtb/700983ab0bde94bed7c645fce770f8e9</a>
There are at least three further alternatives that might be simpler:
2) If you have r_YZ you could use it to compute the sampling variance of the difference between r_XY and r_XZ, that is:
Var(r_XY - r_XZ) = Var(r_XY) + Var(r_XZ) - 2 * Cov(r_XY, r_XZ)
You could then do a univariate meta-analysis on the difference between correlations.
3) If you do not have r_YZ then you won't be able to estimate Cov(r_XY, r_XZ) very well. You could make a guess about r_YZ and then follow approach (1) or (2) above, using cluster-robust variance estimation to account for the possibly mis-estimated sampling-variance covariance matrix.
4) Or you could ignore the covariance between r_XY and r_XZ entirely, fit the model to the long data as you describe above, and use cluster-robust variance estimation (clustering by sample) to account for the dependence between r_XY and r_XZ. This is the quickest and dirtiest approach, and the first thing I would try in practice before moving on to the more refined approaches above.
James
On Fri, Aug 10, 2018 at 9:21 AM Anna-Lena Schubert <a class="moz-txt-link-rfc2396E" href="mailto:anna-lena.schubert@psychologie.uni-heidelberg.de"><anna-lena.schubert@psychologie.uni-heidelberg.de></a> wrote:
Dear all,
I want to run a meta-analysis that compares dependent, overlapping
correlation coefficients (i.e., I want to see if X correlates more
strongly with Y than it does with Z). I already ran a meta-analysis
separately for both of these correlations and would now like to compare
those two pooled effect sizes statistically. Confidence intervals of the
two correlations do not overlap (r1 = .18 [.12; .24]; r2 = .32 [.25;
.39]), but I wonder if there may be a more elegant way to compare these
correlations than just based on CIs.
I wonder, for example, if a factorial variable could be used to identify
those correlations in a "long" data format style, and if I could test
for a significant interaction between variable type (Y vs. Z) and the
correlation in a meta-analysis:
Study Variable r
1 Y .20
1 Z .30
2 Y .34
2 Z .43
I would greatly appreciate if anyone could tell me if that's a good idea
or could recommend other approaches. Thanks in advance for any offers of
help!
Best,
Anna-Lena
</pre>
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<h3 class="auto-style2">Dr. Anna-Lena Schubert</h3>
<p style="line-height: 1;"><img
src="cid:part1.1ED896ED.7358EBB0@psychologie.uni-heidelberg.de"
data-filename="Logo_Diff.png" style="width: 215.5px; float:
right; height: 49.9136px;"><font class="auto-style3"><span
class="auto-style1"><span class="auto-style4">Postdoc at
Section of Personality</span><br class="auto-style4">
<span class="auto-style4">Heidelberg University - Institute
of Psychology</span></span></font></p>
<pre style="line-height: 1;">Hauptstraße 47-51
<span style="line-height: 1;">D-69117 Heidelberg
</span><span style="line-height: 1;">Germany</span></pre>
<pre style="line-height: 1;">Phone: +49 6221 54 7746
Mail: <a class="moz-txt-link-abbreviated" href="mailto:anna-lena.schubert@psychologie.uni-heidelberg.de">anna-lena.schubert@psychologie.uni-heidelberg.de</a>
Web: <a class="moz-txt-link-freetext" href="http://www.psychologie.uni-heidelberg.de/ae/diff/diff/people-schubert.html">http://www.psychologie.uni-heidelberg.de/ae/diff/diff/people-schubert.html</a></pre>
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