[R-meta] Comparing dependent, overlapping correlation coefficients

[Anna-Lena Schubert]

That makes perfect sense, thank you! How would I interpret the same
analysis for a continuous moderator?

estimate se zval pval ci.lb ci.ub var1var2X.Y 0.6192 0.0670 9.2463
<.0001 0.4879 0.7504 *** var1var2X.Z -0.0181 0.1013 -0.1789 0.8580
-0.2166 0.1803 var1var2Y.Z -0.3017 0.1149 -2.6258 0.0086 -0.5270 -0.0765
** M 0.0001 0.0001 0.8208 0.4118 -0.0001 0.0003 var1var2X.Z:M -0.0004
0.0002 -1.6019 0.1092 -0.0008 0.0001 var1var2Y.Z:M -0.0001 0.0002
-0.4270 0.6694 -0.0006 0.0004


I guess this result implies that for each SD (guessing from multi-level
analyses here) of the mediator, the association between X and Z get
slightly more negative than the association between Y and Z. Is there a
way I can test this three-way interaction for significance in the case
of a continuous moderator? I'm also wondering if I should include all of
my relevant moderators in a single analyses or conduct seperate ones.
Interpretation is easier if I look at them separately, but including all
in one analyses might be clearer regarding confounding effects? I also
don't have that many studies in the analyses (21), so I'm not really
sure how many factors I could include in one analysis. What's best
practice here? Thanks, Anna-Lena

Am 05.10.2018 um 17:48 schrieb Viechtbauer, Wolfgang (SP):
> The first output is more difficult to interpret, so I'll go with the second.
>
> You want to test:
>
> H0: X.Z:M0 - Y.Z:M0 = X.Z:M1 - Y.Z:M1,
>
> which is equivalent to:
>
> H0: X.Z:M0 - Y.Z:M0 - X.Z:M1 + Y.Z:M1 = 0
>
> So, you want to use:
>
> anova(res(0,1,-1,0,-1,1))
>
> And indeed, this is testing if the difference between cor(X,Y) and cor(X,Z) is moderated by M (i.e., is different for M0 vs M1).
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: Anna-Lena Schubert [mailto:anna-lena.schubert using psychologie.uni-heidelberg.de] 
> Sent: Monday, 01 October, 2018 14:47
> To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis using r-project.org
> Subject: Re: [R-meta] Comparing dependent, overlapping correlation coefficients
>
> I have recently tried to finish all analyses and have realized that I still haven't fully understood how moderation works here. In the example below, I'm interested in whether the difference between cor(X,Y) and cor(X,Z) is moderated by some factor. From my reading of the metafor examples, var1var2X.Z:M should indicate whether the cor(X,Z) is moderated by M. However, Wolfgang says that term instead describes a moderation of the difference between correlations. I'm perfectly happy to believe him, but I would really like to understand why this is the case. 
>
> In my empirical example the results look as follows:
>
>                 estimate      se     zval    pval    ci.lb    ci.ub     
> var1var2X.Y       0.6580  0.0218  30.1818  <.0001   0.6152   0.7007  ***
> var1var2X.Z      -0.1282  0.0468  -2.7420  0.0061  -0.2199  -0.0366   **
> var1var2Y.Z      -0.2896  0.0480  -6.0315  <.0001  -0.3837  -0.1955  ***
> M1                0.0736  0.0301   2.4474  0.0144   0.0147   0.1326    *
> var1var2X.Z:M1   -0.1648  0.0786  -2.0969  0.0360  -0.3188  -0.0108    *
> var1var2Y.Z:M1   -0.1266  0.0845  -1.4983  0.1340  -0.2922   0.0390     
>
> Here I'm interested in the difference between cor(x,z) and cor(y,z).  Which of these interaction terms is critical to the moderation of this correlation, and why? Also, how can I interpret the direction of the effect?
>
> If I look at another display of the same results, I get an understanding of the moderation, but I'm not sure about a clear test here. Would anova(res(0,1,-1,0,1,-1)) be a sensible test? What I'd really want to test would be if X.Z:M0 - Y.Z:M0 = X.Z:M1 - Y.Z:M1
>
>                 estimate      se     zval    pval    ci.lb    ci.ub     
> var1var2X.Y:M0    0.6580  0.0218  30.1818  <.0001   0.6152   0.7007  ***
> var1var2X.Z:M0   -0.1282  0.0468  -2.7420  0.0061  -0.2199  -0.0366   **
> var1var2Y.Z:M0   -0.2896  0.0480  -6.0315  <.0001  -0.3837  -0.1955  ***
> var1var2X.Y:M1    0.7316  0.0207  35.3007  <.0001   0.6910   0.7722  ***

> var1var2X.Z:M1   -0.2194  0.0483  -4.5437  <.0001  -0.3140  -0.1248  ***
> var1var2Y.Z:M1   -0.3426  0.0491  -6.9767  <.0001  -0.4388  -0.2463  ***

-- 
Signatur


      Dr. Anna-Lena Schubert

Postdoc at Section of Personality
Heidelberg University - Institute of Psychology

Hauptstraße 47-51
D-69117 Heidelberg Germany

Phone: +49 6221 54 7746
Mail: anna-lena.schubert using psychologie.uni-heidelberg.de
Web: http://www.psychologie.uni-heidelberg.de/ae/diff/diff/people-schubert.html


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