In short my question is: Are posterior predictive distributions used in the SEM world? If yes, under which name und for what purpose?

Let be an SEM. Lets say there are a lot of missing values in our observed sample y. We can still get a maximum likelihood estimate for \hat{theta} using FIML. Thus, we get a fitted SEM, or in other words a multivariate normal distribution . Lets now say that I partition my data set y into all values that are missing a and all values that are not missing b. Thus, y=[a b]. I can then get the conditional distribution of a given b using my fitted SEM. A bayesian would call this the posterior predictive distribution.

I understand that in this thread RobK proposes to use the posterior predictive distribution for prediction in this post. Michael gives a first hint that using the posterior predictive distribution might be equivalent to "EM imputation of missing data using the model-implied covariance and means as the imputation model" in this post. Can somebody elaborate on that? Do you know of other techniques that are commonly used by SEM researchers that employ the posterior predictive distribution?

They do now.

http://www.tandfonline.com/doi/full/10.1080/10705511.2015.1014041