This type of modeling is possible, but there are important issues of measurement invariance to be considered. For a recent overview, see
Muthén, B. (2008). Latent variable hybrids: Overview of old and new models. In Hancock, G. R., & Samuelsen, K. M. (Eds.), Advances in latent variable mixture models, pp. 1-24. Charlotte, NC: Information Age Publishing, Inc.
which is on our web site. Essentially, if there is a need for latent classes, these often create measurement non-invariance such that growth modeling is complicated. Growth modeling needs to consider a dependent variable that is in the same metric and has the same meaning across time.
finnigan posted on Tuesday, May 13, 2008 - 1:41 pm
I read the very informative review. However, I don't understand how the addition of latent classes may create measurement non invariance. I would appreciate any steer you might have on this point.
Typically, the measurement intercept (or thresholds) are not invariant across the latent classes. If the latent classes differed only in factor means, but not measurement intercepts, you would have measurement invariance, but this is far less often the case.
RuoShui posted on Thursday, December 12, 2013 - 6:24 pm
It is quite helpful reading the above posts. I am also trying to find out if there are latent classes after analyzing my data using LGCM with multiple indicators.
You said "Typically, the measurement intercept (or thresholds) are not invariant across the latent classes." I am not quite sure if I understand you correctly. Will using the following syntax to constrain everything to be equal across latent classes (except for growth factor means) solve the concern of measurement non-invariance?
You are holding the measurements invariant across classes, including some measurement intercepts. This makes it possible to identify class differences in the growth factor means. But it doesn't solve the concern - this model may fit considerably less well than a model with measurement intercepts varying across classes.
RuoShui posted on Saturday, December 14, 2013 - 6:12 pm
Thank you so much for the explanation. Considering such a limitation of either measurement non-invariance across classes or worsen model fit by holding measurement invariant across classes, is it practically possible to run GMM with multiple indicators? Or is it recommended to always try to run GMM with observed outcomes?