I am wondering about your recommended procedure for looking at a latent class model in tandem with a mediation model. In particular, I am interested in using a latent class variable as an IV in the mediation model. I recognize that including the mediating variable and outcome variable as indicators of the latent class membership would be similar to modeling the regression pathways of the mediator and outcome on the latent class (i.e., 'x ON c'), and would be able to include a regression of the outcome on the meditator (as per Example 7.20 in the User’s Guide). This would then suggest, at least to me (but I could be very wrong!), that the pathways required to examine a mediation model would be present. Further, as per Example 7.20 of the user's guide, this regression pathway between the mediator and outcome would vary across classes, and would thus suggest a moderating effect. I am hoping you might be able to advise about how to go about testing for a mediating effect (either across classes or within classes).
Any recommendations or references you may be able to provide me with would be greatly appreciated.
It makes sense to have a latent class variable as the X variable in an X, M, Y mediation model. Take the example of a binary latent class variable, which is then like a binary X. Your model specifies Y ON M. The effect of X on M is the difference in means of M over the two classes (that's what a slope of M regressed on a binary X gives). So you get an indirect effect as the product of the Y ON M slope and that difference. You can express that via Model Constraint. The direct effect of X on Y is a mean difference in Y for the two classes.
Thank you for the prompt, and insightful response. However, what M and Y differences would one focus on with 4 latent classes? In this case there would be six mean differences for both M and Y. Further, because the Y ON M slope may differ across classes, one could calculate 12 indirect effect values. This is a mock-up of my MODEL command and my MODEL CONSTRAINTS. Would you be able to advise as to which of the M and Y differences, and indirect effects might be of most interest?
I would pick a reference category for your 4-class IV and compare to that, so with e.g. 4th class being the reference, you would look at m1-m4, m2-m4, m3-m4, and similar for the O's. Your setup is otherwise what I had in mind.
For anybody else that is interested in this thread: if the research questions involve estimating a class model and then adding mediators, outcomes, etc. without changing the class model you may be interested in reading Tihomir & Bengt's Webnote #15 (http://www.statmodel.com/download/webnotes/webnote15.pdf) or the associated manuscript: Asparouhov, T., & Muthén, B. (2014). Auxiliary Variables in Mixture Modeling: Three-Step Approaches Using Mplus. Structural Equation Modeling, 21, 1–13. doi:10.1080/10705511.2014.915181 for how to fix the model parameters at the correct values. The details are also discussed in: Nylund-Gibson, K., Grimm, R., Quirk, M., & Furlong, M. (2014). A Latent Transition Mixture Model Using the Three-Step Specification. Structural Equation Modeling, 21, 439-454. doi:10.1080/10705511.2014.915375