In a series of papers, Bob Mislevy outlined procedures for exploring the variance in a latent trait across manifest subpopulations and the covariance of the latent trait with manifest collateral variables. For example, based on NAEP math assessments, what is the difference in math abilities between boys and girls? His approach shrinks individual scores toward model-based expectations. The scores are sampled from a posterior distribution and can then be fed to analysis programs like Wesvar and HLM. The collateral variables used in shrinkage can differ from those used in analysis.
Can MPLUS be used to create such scores? If so, any examples?
Mislevy's NAEP approach is akin to multiple imputation for the latent ability variable (which is the missing data). The current Mplus version does not yet generate multiple imputation data. Mplus can, however, analyze multiply imputed data and summarize the results properly.
An alternative that is feasible when the item structure is not too large and complex is to do the analysis in a single step, directly estimating regressions involving the latent ability variable.
The disadvantage with a single step is that one is not free to use a richer set of variables in the shrinkage of the ability estimates than what one wants to use in the regression model. Such a procedure is of interest to me because I am analyzing an experiment in which there are post-randomization covariates which I would like to use to reduce the uncertainty about each person's ability but which if used in the regression would remove some treatment effects.