I'm performing a latent class growth mixture model according to the framework laid out in Jung and Wickrama 2008 (An Introduction to Latent...). They recommend to start with an unconditional LCA and comparing fit indices to establish an optimal number of classes, then move onto a conditional GMM.
However, I'm getting somewhat incompatible fit stats between the LCA and GMM.
Basically, in the LCA, I have good fit at a four class solution based on BIC, VLMRT, LMRT, entropy, and BLRT. I then examine a four class solution with an unconditional GMM by freeing the i and s parameters (holding q fixed), and get lower AIC/BIC/ssBIC, a comparable entropy (decreased by .001 from .917 to .916, still very high), but my VLMRT and LMRT jump from p<0.000>.22 in the GMM model. BLRT stays 0.000 across LCA and GMM models.
The main question is this: Given quantitative (LCA fit stats) and theoretical evidence supporting four classes, does it make sense to consider the k/k-1 based VLMRT/LMRT values when assessing GMM models? Or should I be starting from the ground up with GMM and comparing 1...n class solutions with my parameters freed?
I was thinking that the LCA indicates four classes, the VLMRT/LMRT tests are primarily used for class count differentiation, therefore they are not necessary to consider in the GMM (or any further analyses).
Ok, so when you say LCA that means LCGA. So without within-class variances for the growth factors compared to GMM with those variances. Those are quite different models and I wouldn't draw conclusions about one from results of the other. You would expect BIC to improve. I would rely on BIC alone, comparing different number of classes in the unconditional GMM.