Is it possible to have different slope loadings for within and between levels for multilevel growth mixture model? How should we interpret the results when getting different loadings at within and between levels?
In order to estimate the non-linear growth, I set the model slope loadings by doing the following, freely estimating the loadings for W3 and W4 at both within and between, but constrain them to be the same across levels. However the resulted loadings don't make much sense to me; but if I don't constrain the loadings to be the same, I get different slope loadings for w3 and w4 at each level, the loadings at between level makes more sense, but the within level's loading is different and I am not sure how to interpret the loadings at the within level.
It is best to hold them equal across levels - if you don't, you are not doing regular (3-level) growth modeling. This is because the mean structure enters on the between level and growth models have the same time scores for the mean structure and the covariance structures on within and between.
Thanks so much for your timely advice! I finally got the syntax work--somehow I wish the earliest version of Mplus syntax is also available in the manual--MPlus has simplified the process of fitting growth model a lot and it's a great advantage of the software; at the same time the "source code" can still be very useful when doing something "extra" ^_^
See pages 602-607 of the Version 6 user's guide to see the correspondence between the BY and | growth modeling specifications. Note that the defaults for the | language are appropriate for growth models whereas the defaults for BY are appropriate for factor models. I suggest using the | language for growth models for this reason.