I have conducted a traditional latent growth model and a latent class growth analysis on the same data that models parallel processes. The LGC analysis demonstrates significant intercept and slope variance and the data tend to suggest a 6 class solution.
When I regress the intercept and slope parameters on a set of covariates, the results are substantively different than when I regress the latent class membership on the same set covariates. Are there particular situations when this would be expected in the data?
I assume that your "traditional latent growth model" (GM) is a single-class model (and not a mixture - i.e. GMM) and that the latent class growth analysis (LCGA) is a mixture model with zero within-class variation. If so, the LCGA classes can be seen to represent trajectory shapes defined by combination of growth factor values (e.g. high intercept, low slope vs low intercept, high slope). Because covariates of LCGA class membership predict such combinations of growth factor values, they will show different influence on the latent class variable than they would show in their influence on each of the growth factors in a GM.