[R-meta] Computing var-covariance matrix with correlations of six non-independent outcomes

[Mika Manninen]

Hello,

I am doing a meta-analysis looking at the effect of a teaching intervention
(versus control) on six types of motivation/behavioral regulation.
Theoretically and empirically these constructs form a continuum in which
the continuum neighbors are most strongly positively correlated and the
furthest from one another most negatively correlated.

I have 95 effects. These effects come from 25 studies, each reporting
scores for between 1-6 motivation types. The number of effects per
motivation ranges from 22 to 13. In some studies, they have measured only
one or two types whereas in others they have measured 5 or all 6 types of
motivation.

I originally ran a separate random-effects meta-analysis for all the six
outcomes. However, I got feedback that the dependency of the motivation
types should be taken into account and a 3-level meta-analysis was
recommended. After looking into it, the 3-level model seems to be a worse
approach than the multivariate approach.

As is not usually the case, I have succeeded in gathering all correlations
between all the motivation types for all studies (some from original
reporting and some from previous meta-analysis findings).

My question is, how do I compute the V-matrix for this data in order to run
the multivariate analysis? I read the whole archive but I could not find a
clear answer to the problem.

Thank you very much in advance,

Mika

	[[alternative HTML version deleted]]