I have run LCA for a number of risk factors with best fit 5 classes. Now I want to know whether a particular risk factor (used in the LCA) better predicts distal outcome X in and of itself, or only when it occurs within the context of the other risks that fall into its LCA class. Does that make sense?
That is, let's say the LCA is by Var1-Var15, and that Vars1-5 come together to C1. Now I want to know if:
Var1 predicts distal outcome X better within the context of Vars2-5 (ie. within C1) than it does alone.
Is that possible? I have saved the data and made myself a file (weighted by probs), but if I look at Var1 predicting outcome moderated by LCA I am surely getting into multicoll problems. So I figure I need to build it into the MPlus model some how.
My impression is that doing what you suggest would tell me the prediction from the indicator to the distal outcome (and that I could constrain/unconstrain it to be equal or not for different classes) but not quite answer my question. That is, what I really want to know is whether the predictor has a greater prediction as a function of the probability of it occurring with the other risks in the class than it does alone. An example might help, it's hard to write down!
So, say I have lots of risk factors and I find a class (C) that includes higher probability of poverty and divorce...and that C predicts the outcome, depression. What I want to find out is statistically whether poverty predicts depression per se, or better in the context of divorce (i.e. within C). I kind of want to see whether C moderates the impact of poverty on depression, but of course I can't do that because poverty is part of how C is estimated...
I think it would be hard to use a mixture model to estimate if poverty predicts depression better in the context of divorce than alone. But regressing depression on poverty, possibly with class-varying slopes, does tell you if poverty has an influence on depression over and above that of class membership.
A totally different alternative is to skip the mixture part and simply work with interactions among poverty, divorce etc in their prediction of depresssion.