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Hi Mike and metaSEM users,
First of all, thank you, Mike, for maintaining such an active presence on this forum! It makes a HUGE difference as a user to be able to get questions answered from the package maintainer within a pretty reasonable timeframe. :)
I had another question about the meta-analytic indirect effects that are estimated by indirectEffect() (and then meta-analytically combined using meta() ).
As most people already know, in a single sample, a mediation model can be represented as a path model in the attached image. This path model can be represented using the following two regression models:
(1) M ~ aX + e_1
(2) Y ~ bM + cX + e_2
The direct effect of X on Y, not through M, can be estimated using c and the indirect effect of X on Y through M can be estimated using the product ab.
For a meta-analysis I'm doing, I wanted to present coefficients a, b, and c so that readers could understand the relative contributions of a and b to the indirect effect. I had thought that a good way to do this would be to estimate the meta-analytic pooled correlation matrix using tssem1(), which I could use to find meta-analytic coefficient a, and fit the regression model (2) with this pooled correlation matrix using tssem2(), yielding coefficients b and c. You can find my code using 10 arbitrary correlation matrices attached.
My problem is that the product ab calculated using the method I described above departs quite substantially from the meta-analytic indirect effect estimated by first calculating the indirect effect within each correlation matrix, then pooling these indirect effects. The coefficient c obtained from tssem2() also departs from the direct effect obtained from indirectEffect() and meta(). I haven't done a formal simulation study, but I've played with different correlation matrices and found that the indirect effects estimated in these different ways depart from each other pretty consistently.
What's going on here? Is there a flaw in my thinking? Is there a better way of obtaining meta-analtyic estimates of the quantities a, b, and c?