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 [8] RobK proposes to use the posterior predictive distribution for prediction in this post [9]. 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 [10]. Can somebody elaborate on that? Do you know of other techniques that are commonly used by SEM researchers that employ the posterior predictive distribution?