Factor scores
Message/Author
 Anonymous posted on Saturday, September 17, 2005 - 5:36 pm
Hi, Can factor scores be saved for type=imputation? I am testing a CFA for ordered categorical data. There is no problem saving the scores when a single imputed data set is used, but there is a problem with saving for the run with the multiple data sets. thanks!
 Linda K. Muthen posted on Sunday, September 18, 2005 - 3:10 pm
This can't be done currently. We will add it to our suggestion list if you send an email requesting this to support@statmodel.com.
 Mario Lawes posted on Tuesday, September 24, 2019 - 1:31 am
Hi,
how are the factor scores estimated using the ml estimator when missing data is present?
My understanding is that fiml is used to estimate the structural parameters and then the regression method is used to estimate the factor scores.
However, I was not able to find any formulas for the factor score estimation with missing data. I am also interested in how the correspoding standard errors are computed. I see that for each missingness pattern a seperate standard error is computed.
Thank you!
 Tihomir Asparouhov posted on Tuesday, September 24, 2019 - 3:30 pm
Take a look at Appendix 11

If eta represents the factors, the factor score estimates are the posterior means

E(eta | non-missing Y, X, estimated model)

and the standard errors are the square roots of the diagonal elements of the posterior/conditional variance

Var(eta | non-missing Y, X, estimated model).

If you want to replicate the computation you would have to compute the model implied joint distribution of eta,Y,X which is a multivariate normal say with mean Mu and Sigma. For a particular missing patter you would reduce these matrices to exclude the missing values and then compute the conditional distribution for eta given the observed values using
https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Conditional_distributions