Jan Ivanouw posted on Wednesday, March 21, 2012 - 5:15 am
I am wondering how the class probabilities are calculated in a mixed model (with no covariates, in order to keep things simple). In part 2 in the paper Lübke and Muthén "Investigating population heterogeneity with factor mixed models" (2005) it is mentioned that class probabilities are calculated using multinomial regression. Is this a different approch for calculating class probability than in a LCA (without any latent continuous factor), and which terms are used in this multinomial regression?
In the paper is also mentioned A as a parameter describing how class membership influences eta. Is this A the same as the parameter Alpha (C) given in the Mplus output from a mixed model?
In a model with no covariates, there is no multinomial regression. See the class proportions in the results.
Class membership influencing a factor is seen in the factor means varying across classes.
Jan Ivanouw posted on Wednesday, April 04, 2012 - 6:22 am
Thank you. What I wonder is this:
Class probabilities for a LCA-model are calculated as described in appendix 8 of the Technical appendices.
It seems, though, that this method does not work quite the same way with FMM-model (of type FMM-2 in Clark, Muthen et al. - branch 1 of the paper Muthén, 2008 Latent variable hybrids) I would like to ask how are class probabilities calculated for the FMM-model?
There are no explicit formulas for this as numerical integration is required. The following paper which is available on the website might help:
Muthén, B. & Asparouhov, T. (2009). Growth mixture modeling: Analysis with non-Gaussian random effects. In Fitzmaurice, G., Davidian, M., Verbeke, G. & Molenberghs, G. (eds.), Longitudinal Data Analysis, pp. 143-165. Boca Raton: Chapman & Hall/CRC Press.