Mark,
The formulas needed to calculate the covariances are given in the
following reference:
Olkin, I., & Finn, J. (1990). Testing correlated correlations.
Psychological Bulletin, 108(2), 330?333.
Unfortunately they're a bit complicated, a pain in the rear to program,
and sometimes return non-positive definite covariance matrices that create
problems at the meta-analysis stage. If you've got the raw data, a cleaner
approach would be to use a basic bootstrap (i.e., re-sampling cases) for
the set of correlations you want to meta-analyze.
But a larger question might be relevant here: what is the goal of
conducting a multi-variate meta-analysis on these correlations? Is it to
come up with a synthetic correlation matrix? To understand heterogeneity
across studies in the correlations? Depending on your answer--and given
that you have access to the raw data--other statistical approaches (other
than MV meta-analysis) might be equally or better suited for the problem.
James
On Wed, Jan 17, 2018 at 9:17 AM, Mark White <markhwhiteii at gmail.com>
wrote:
Hello all,
I have 8 studies in my dissertation; I want to meta-analyze the
correlation
between focal variable X and outcome Y. Let variables for Study 1 be x1
and
y1, Study 2 be x2 and y2, etc. However, I also have *various measurements
*of
each construct in some studies. For example, in Study 1, I have the
correlation between x1_1 and y1_1, as well as x1_2 and y1_2. And in Study
2, I have the correlation between x2_1 and y2_1 as well as x2_2 and y2_2.
In Study 3, I have these all the way up to x3_10 and y3_10.
I want to perform a multivariate meta-analysis, since I have all of the
raw
data. My question: How do I calculate the covariates between these
correlations? I know I want to end up with a covariance matrix where the
diagonal is the variance, off-diagonal the covariances (with all zeros
where they are from different studies). In the analysis examples on the
metafor website, these are already calculated for the user. How do I
calculate these from my raw data?
Thank you,
Mark
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