Jon Heron posted on Friday, July 09, 2010 - 3:23 am
I'm carrying out an unconditional LCA, exporting the posterior probs to use as a weighting in my second stage covariate analysis (to prevent the covariates affecting the class derivation). I have missingness in my covariates as well as my dependent variables and I'm comparing the results of two ways of dealing with missingness.
1] ICE then LCA Impute multiple datasets (using ICE in Stata) and fit the LCA model to each one in turn. I am not allowing Mplus to pool the LCA results (Rubin-style) due to earlier problems with this (already discussed with Bengt in another post).
2] LCA then ICE Fit one LCA model in Mplus with FIML and export those results, using the single set of posterior probs as a weighting in my ICE imputation.
As one might have predicted, the parameter estimates in each approach are similar as I used 100 imputations (I have been uncharacteristically patient), but the SE's for approach  are considerably higher to reflect the variability in LCA results between each dataset.
Despite the fact this outcome is not surprising, I am still at a bit of a loss as to how to finish this up. Is  superior as I have maintained the uncertainly that approach  would lose when manifesting my latent measure, or do they both have their shortcomings.
You can do the imputations in Mplus using the SEQUENTIAL method (Ragunathan's method) without having to go outside Mplus to ICE in Stata.
Regarding 1], I am not clear on how you combine the results to compute the SEs - not by Rubin's formula you say, so do you just take the average SE?
Regarding 2], I think this only works well when the entropy is high (say > 0.8).
Another imputation-oriented method is to use the LCA indicators only and create plausible values for the latent classes using the new Version 6 option for that. Then do multiple regressions of class on covariates.
Yet another approach is to first estimate the model with covariates influencing class membership, using ML, and include the covariates in the model so that missing data on them is handled by MAR. Then use SVALUES to carry those estimates over as fixed starting values for a Bayes analysis that simply generates the missing data. Then analyze the model you want.
As an aside, when you impute for the covariates, perhaps you don't want to use the LCA indicators given that in the modeling you don't want covariates to affect class formation.
Jon Heron posted on Monday, July 12, 2010 - 1:39 am
Re  sorry for not being clear, I don't pool the results in Mplus, I use MIM to pool them in Stata. I meant that it is my covariate*latent-class parameter estimates which are being pooled, rather than the latent-class posterior probs. I expect if I were to pool the results of the LCA prior to my multinomial model, then SE's for the covariate effects would be reduced and be more similar to those obtained in . If I were to chose this option, what would I average over the imputations - the pattern specific assignment probabilities?
Re  My entropy is pretty good ~ 0.85. With this approach I do drop the latent class indicators prior to the imputation step.
It seems I am spoilt for choice here thanks to Mplus 6. Unfortunately I am under some pressure now to finish up and move on
Rachel Ellis posted on Wednesday, January 15, 2014 - 6:22 pm
Hello, I'm running a longitudinal growth mixture model, using FIML to deal with missing data. I've also used multiple imputation on auxiliary variables (that I've analysed with DCON in version 7.11) to get their means and S.E.'s. Some articles have suggested that data imputation isn't appropriate with LCGA/GMM, because they assume multiple subpopulations whereas imputation assumes a single population (e.g. Costello, D. M., Swendsen, J., Rose, J. S., & Dierker, L. C. (2008). Risk and protective factors associated with trajectories of depressed mood from adolescence to early adulthood. J Consult Clin Psychol, 76(2), 173-183. doi: 10.1037/0022-006X.76.2.173).
Just wondering if anyone has any thoughts on this? Thanks