I have created a meta-analytic correlation matrix using sample and reliabilty corrected correlation values between 15 varaibles. I also calculated harmoic mean but I am unsure how to calculate mean and SD to use the correlation matrix as input for SEM. Any suggestions would be highly apprecaited.
Dear Dahlia,
meta-analytical SEM (MASEM) has experienced quite a development in recent years. I can recommend these papers as a good starting point:
Sheng, Z., Kong, W., Cortina, J. M., & Hou, S. (2016). Analyzing matrices of meta-analytic correlations: Current practices and recommendations. Research Synthesis Methods, 7(2), 187-208. doi:10.1002/jrsm.1206
Wilson, S. J., Polanin, J. R., & Lipsey, M. W. (2016). Fitting meta-analytic structural equation models with complex datasets. Research Synthesis Methods, 7(2), 121-139. doi:10.1002/jrsm.1199
As you will see, it is not really necessary to manually calculate the correlation matrix as especially Wilson et al. recommend to run a multi-level random effects model with cell-dummies as predictors and excluded regression intercept to create the correlation matrix. Sound strange. It will be straightforward if you have read the paper.
With regard to the N, more recent approaches to not take the mean for calculating the overall sample size as the mean would result in an N too low for some of the cells and too high for others. Instead, The MASEM is run with WLS as an estimated in which the cell-specific N's are taken into account to estimate proper standard errors.
As a sample size for the overall model (e.g, model fit), the SUM and not the mean is used as this is more appropriate (actually this many cases were investigated by the studies).
By the way: The Wilson paper recommends a very fancy idea to calculate a correlation matrix adjusted for moderators. However, after one tedious try I gave up applying their idea as reviewers won't understand and accept it anyways (and it did not make a difference in my case).
HTH
Holger
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