Hi, forgive me if you see duplicate messages. I previously posted the question on my last thread. But I think it's more proper to make it as a new topic.

My question is like this：Since I want the missing value of my dataset, whereas FIML doesn't provide that, I chose multiple imputation (MI) to deal with my missing data instead of FIML. The problem is after MI (say, I did 5 imputations), I get 5 imputed datasets. How can I use these datasets to build SEM? Shall I conduct SEM on each imputed dataset separately? If so, how can I combine the model parameters and model fitness indice (e.g. TLI, CFI, RMSEA)?

I find there is one previous thread in this forum talking about the same problem: https://openmx.ssri.psu.edu/thread/118 . It tells that OpenMx cannot deal with the multiple imputed datasets directly, we need to do the combination manually. Can I know the details how to do this manually? Do we conduct SEM separately on each imputed dataset and average all the parameters and weights? Thanks in advance.

The long and short of it is that you would fit your model(s) to each imputed dataset. Your overall point estimates would be the averages of each dataset's vector of point estimates. The overall repeated-sampling covariance of the point estimates would be the sum of two matrices. The first matrix is the average of the datasets' repeated-sampling covariance matrices; this represents the average "within-dataset" estimate of sampling variability. You would create the second matrix by subtracting the average point-estimate vector from each datasest's point-estimate vector, taking the outer product of that difference vector with itself, and averaging those outer products across datasets. This second matrix represents the "between-dataset" sampling variability. Once you have the overall repeated-sampling covariance matrix, you can (for instance) get standard errors by taking the square roots of its diagonal elements. This paper by Don Rubin might be useful to you.

I don't know that much about MI, especially in a SEM context, so I can't say much more than that. I would imagine that you could likewise average model-fit indices, but there may be interpretational complications I'm not aware of.