I have a question about the output for Bayesian analysis via the Gibbs sampler. When conducting a BSEM measurement model, If one requests 'RESIDUAL' as an output option Mplus will provide the implied model covariance output. In running these models I am utilizing the standardize command on all manifest indicators, so this implied covariance matrix should closely approximate a correlation matrix.
My question is being Bayesian, it would seem that the implied covariance matrix has an underlying distribution itself. If one uses the mean or median estimates of the lambda, phi, and theta matrix to solve for the implied covariance matrix via the factor analysis model the results rarely coincide with the output provided by MPlus. Is Mplus solving for the implied covariance matrix at each iteration and then providing a mean or median point estimate at output? Is this point estimate the same one as specified in the analysis properties or is it independent?
Thanks for any feedback, trying to resolve something with a co-author for a journal article.
In the residual output we provide the implied covariance matrix using the point estimates for the model parameters. If you want to obtain the distribution for the implied covariance matrix and median/mean estimates for that you can use model constraints to define the implied variance covariance parameters. If there are covariates in the model the residual output uses the sample statistics for the covariates.