I have modelled latent growth trajectories, and came up with a four group solution in which groups differ for intercept and slope.
I would now like to explore the relationship between external variables and intercept and slope of these trajectories.
So far I have run a mixture model in which I estimate the trajectory classes and regress slope and intercept on the external variables. However, of course this changes my original trajectories which I would actually like to keep. I do not want to estimate the trajectories dependent on my external variables, rather I want to determine whether intercept and slope are influenced by these external variables.
I have also looked into the known class option, but of course if I put the trajectories into the model as known classes there is no intercept/slope to be regressed on my external variables.
I would save membership in trajectories based on most likely class membership as described in the handbook and then do your regression analysis as intended. However, this would be a very rough and dirty approach, especially when your classfication quality is not very high. And may be, some of your "external" variables also influence class membership "C". A better approach would be to correctly specifiy a conditional growth mixture model, testing direct effects of variables on indicators and then rely on this (hopefully) correctly specified solution. There are some articles in the growth mixture section (articles) on the mplus web site that discuss your problems.
Thanks very much for your reply. Your first point is what we meant by trying known classes, but what we want to do is to see how our external variables are able to explain the different intercepts and slopes on our existing trajectories. As we have existing trajectories we are not not modelling intercept and slope and so we have nothing to regress on.
For your second suggestion, we don't want to estimate trajectories conditional on these variables, we want to link not class membership, but class intercept and slope with these external variables.
You say that you want to relate external variabls to intercepts and slopes without the externals influencing the model. I am, however, unclear if you want to study the relationship (1) between external variables and the latent class membership - which implies that you are studying the relationship of the external variables to the class-specific means of the intercepts and slopes - or (2) the relationship between external variables and within-class variation in intercepts and slopes.
Regarding (1), external variables can be studied with respect to latent classes using auxiliary "e" or "r" if you have high entropy.
If your model changes quite a lot when adding external variables as predictors, it seems worth examining why that happens.