Hi Jian-Bin,

You could ask the developer of the package directly, Mike Cheung. In my experience, he responds to these types of inquiries quite fast.

0) I'm not sure you will reach the results that you want with metaSEM, primarily because the number of studies that you have is quite low. However, you can give it a go.

1) I would advice against it. Problem is that the correlation coefficients will not only be used to construct the meta-analytical correlation matrix, but also the variance-covariance matrix. It is not clear if this latter matrix is valid with partial correlation coefficients, in particular as the package will assume they are zero-order correlations.

2) Not directly as you can easily in metafor, for example, with random coefficient structures. If appropriate, you might model two outcome variables loading on a latent outcome variable and allowing the dependent outcomes errors to covary.

Thank you very much Robert. 

I will try contacting the developer. Just one follow-up question from your answer (2), modeling two outcome variables as a latent construct will give me a regression coefficient, which I think is different from zero-order correlation coefficient. In this sense, can it be used in the metaSEM? 

Jian-Bin,

metaSEM uses two stages for modelling. In the first, you simple pool the zero-order correlation coefficients to extract the matrices as I described. In the second, you estimate a structural model based on those matrices. You can hence include latent constructs in the second phase without worrying about them in the first. This would still allow you to use zero-order correlations for effects on related outcomes by modelling the related outcomes as a single latent construct. 

Note that the outcomes of metaSEM are always gamma (or regression) coefficients and not zero-order correlations.

Robert,

Thank you. I assume the method you proposed is the correlation-based metaSEM, while what I wish to use is the parameter-based metaSEM because I would like to see how strong is the indirect effects across studies. But anyway I thank you for your kind notice that I could fit a latent construct model in the second phase. 

I'm sorry, I didn't pick up on that. I don't think it's common to refer to parameter-based MASEM as metaSEM. The latter points specifically to Mike Cheung's package. But perhaps I am mistaken.

To my understanding, you may run into two issues when trying to conduct a parameter-based MASEM. 1) if you have missing effect size: you require the predictor, mediator, and outcome across all studies. 2) Your model cannot be overidentified, but works well if it is just identified. If you run any kind of CFA or SEM (or follow my suggestion for a latent variable to model dependency between outcomes), you will get a different model-implied correlation matrix, it doesn't fit the data.