[R-meta] Handling dependencies among multiple independent and dependent variables

[Viechtbauer Wolfgang (SP)]

Ah, I see what you mean. Well, not sure about the TSSEM approach (Mike/Suzanne would know this better), but the approach I described (which is in essence the GLS-type approach described by Becker) handles 1) just fine. Actually, to be precise, it handles the case where only cor(x1,x2), cor(x1,x3), or cor(x2,x3) are reported or all three, but you have a problem when only cor(x1,x2) and cor(x1,x3) are reported (or any other pair), because then you cannot compute the covariance between the two correlations since that requires knowing cor(x2,x3) (or whatever correlation is missing). But let's say every study only reports one of the three correlations, then the GLS approach does allow you to construct a full 3x3 matrix (at least from a practical point of view - not sure how meaningful such a correlation matrix then is).

Best,
Wolfgang

-----Original Message-----
From: Jens Schüler [mailto:jens.schueler at wiwi.uni-kl.de] 
Sent: Sunday, 25 March, 2018 13:12
To: Viechtbauer Wolfgang (SP); r-sig-meta-analysis at r-project.org
Subject: AW: Handling dependencies among multiple independent and dependent variables

Hi Wolfgang,

the pooled correlation matrix doesn't have any empty cells but the way I
understood it is that you require at least one study that reports
correlations between all the variables you are interested in to use the
TSSEM approach of Cheung.

e.g. you are interested in 3 variables and you have 3 studies.
Now, there are two possible situations:
1) None of these 3 studies report all 3 correlations but only 1 or 2
correlations. However, when pooled, the matrix doesn't have empty cells
2) At least 1 or more studies report all 3 correlations

As I have understood it, these situations appear to matter, with the TSSEM
approach only to be viable in situation 2.
Should this statement turn out to be unfounded/debatable, I could ditch the
old approach in favor of TSSEM.

Best
Jens 

-----Ursprüngliche Nachricht-----
Von: Viechtbauer Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> 
Gesendet: Sonntag, 25. März 2018 11:50
An: Jens Schüler <jens.schueler at wiwi.uni-kl.de>;
r-sig-meta-analysis at r-project.org
Betreff: RE: Handling dependencies among multiple independent and dependent
variables

If you want to pass a pooled correlation matrix to some kind of software for
SEM and one of the cells is NA, then indeed, this won't work. Depending on
the model you are trying to fit, certain cells may actually not be needed,
but I don't know any software for SEM that will work with a
covariance/correlation matrix with missing cells.

Best,
Wolfgang

-----Original Message-----
From: Jens Schüler [mailto:jens.schueler at wiwi.uni-kl.de]
Sent: Saturday, 24 March, 2018 20:57
To: Viechtbauer Wolfgang (SP); r-sig-meta-analysis at r-project.org
Subject: AW: Handling dependencies among multiple independent and dependent
variables

Dear Wolfgang,

thank you very much for the detailed explanation. 
I just have to rearrange the coding sheet a bit and I am good to go. The
project we are working on is actually a MASEM and I am currently tackling
the stage of pooling the correlation matrix. However, we are not using the
TSSEM approach of Cheung but follow the "old" approach of Viswesvaran &
Ones, 1995.

I would like to raise a quick question concerning the applicability of the
TSSEM approach. I am not sure whether Cheung stated it himself, in one of
his articles or book, but others (e.g. Landis 2013; doi
10.1007/s10869-013-9285-x) argued that TSSEM can only be used if at least
one study provides full information - which is not the case in our project. 
Is this really a "hard/must" requirement or what would be the risk/danger if
TSSEM is used nevertheless in such a scenario?

Best
Jens