[R-meta] Calculating covariances in multivariate meta-analysis

[James Pustejovsky]

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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