I've looked through both the paper and the technical appendices, including the Mplus input files, and I cannot find an example of mediated moderation under the following conditions:
Y = latent class variable (a growth mixture) X's = set of continuous variables (including a defined moderation term) M = continuous variable
I'm mainly interested in using an indirect statement to examine the mediated effect of the moderation term (X3) on class membership. The closest example in the paper uses a measured categorical outcome, but I'd prefer not to export classifications for subsequent use.
There are two classes. I've already established that there is a significant moderation effect (i.e., that the interaction term is associated with the latent classification variable), and I'd now like to test whether that moderation effect operates indirectly and/or directly. I've considered just using the posterior probability of membership in the high risk trajectory as my outcome. However, I only want to do that if it's not possible to simultaneously model everything using some combination of syntax for mixture models and indirect effects. Perhaps something like the following, though I'm not sure how to indicate that I'm interested in IND within the OVERALL model:
With only 2 classes, you can apply the same approach as with an observed binary outcome, which is discussed in the causal-effects paper Linda referred to. The paper and the Mplus setup for this are on our web site.
I know that I can use the hard classification as an observed binary outcome, but to do so disregards the probabilistic nature of the latent class variable. I'm pretty sure that I don't want to do this. One potential compromise would be to use probability of membership in one of the two classes as a quasi-continuous outcome. So, two questions to follow up:
1) Is it possible to use the actual latent class variable (i.e., in a single stage analysis), rather than a saved hard classification or posterior probability (i.e., a two-stage analysis)?
2) If the single stage analysis is not possible, what are the implications of using a hard classification versus using a posterior probability of membership in a two-stage model?