I am in the process of modeling covariates and distal outcomes with a latent profile model (3-classes). As in p.182 of the Mplus User's Guide (example 7.17), my distal outcomes are latent factors.
I used the BCH method to simultaneously estimate covariates and distal outcomes in the latent profile model (Asparouhov & Muthen, October 7, 2014 - auxiliary variables in mixture modeling: Using the BCH method in Mplus to estimate a distal outcome model and an arbitrary secondary model).
I fixed the mean of the distal outcomes to 0 for one of the classes to examine differences in mean across classes. Unit variance identification was used to set the scale for the distal outcome factors. The class-specific means, SEs, and significance tests appear and the needed information is provided.
The problem begins when I attempt to include a command to regress distal outcomes on the covariates in the %OVERALL% section (e.g., distal ON covariate). I want to control for the relations among covariates and distals before class-specific means are estimated.
Although the model runs, it no longer provides class-specific estimates of distal outcome means. It only provides the mean and relevant estimates for the observed indicators for each class.
I was wondering if I could get your thoughts on how to address this issue? Thanks in advance!
Thanks-- yes, Tech4 provides the distal means for each profile. I'm curious why the mean estimates from tech4 and the class-specific intercept values (that represent distal outcome means now that they are endogenous variables) are different. This seems to be due to the distal outcome means (intercepts) now being conditioned on class AND the three binary covariates that I have in the model. Is that correct?
Also, in this model (similar to figure 2 in webnote 15, plus a path from c to x), do you have any suggestions in how to summarize distal mean differences conditioned on class and covariates? I am most interested in mean differences across classes, but can't ignore the covariates (and centering doesn't seem appropriate since they are binary).
Q1. Yes, it is the usual difference between means and intercepts. You might center the covariates.
Q2. For ideas, see e.g. the paper on our website
Muthén, B., Brown, C.H., Masyn, K., Jo, B., Khoo, S.T., Yang, C.C., Wang, C.P., Kellam, S., Carlin, J., & Liao, J. (2002). General growth mixture modeling for randomized preventive interventions. Biostatistics, 3, 459-475. Mplus inputs and outputs used in this paper can be viewed and/or downloaded from the Examples page.
Thanks for these prior responses. I have another question.
When simultaneously modeling covariates and distal outcomes in a latent class model using the BCH method, is there a way to quantify the additional variance in distal outcomes explained by C, beyond what is explained by D on X?
C plays the same role as a dummy variable (or dummy variables for more than 2 classes) in regular linear regression. The regression slopes for the dummy variables are obtained from the difference in the distal means for the different classes. Thereby it should be possible to compute an R-square. But that seems like a lot of work when you already see that C makes a significant difference.