I would be grateful if someone could explain me what is the "true" difference between the random effect models and the latent growth curve models. For me they are equivalent ... It seems to me that the difference comes from the fact that these two models are used in separate fields. If the answer to my querry is that the random effect model is a particular case of the latent growth curve model, then I would be grateful to know which practical situations one can use the latent growth curve model but not the random effect model?
The multilevel (HLM) and mixed linear (SAS PROC MIXED) models are identical. The SEM random effects model differs from those models in two ways: the SEM model has time scores as parameters rather than data and time-varying covariates cannot be random in the SEM model. If you want to see a comparison of the formulas for the three models, you can purchase the latest Day 2 short course handout where this is described on slides 25-32.
Note that in Mplus, time scores can be treated as parameters or data (individually-varying times of observation) and time-varying covariates can be random.
Thanks a lot for your thoughts. But I still have a problem in understanding your statement. First, the linear mixed effects model are also considered as conditional models in the sense that covariates are considered as exogeneous and no distributional assumptions are made for them. My question still holds: In which practical situations one can use the latent growth model but not the linear mixed effect model.
PS: When I speak about the linear mixed effect model I speak about the modelling point of view and not the software used to estimate it.
I would also to thank you for this interesting discussion list.
I am speaking of the models not the software. I refer to the software for those not familiar with the names of the model.
As I said earlier, the three models are statistically equivalent with the exception that in the SEM model time scores are treated as parameters and in the SEM model the slopes of time-varying covariates cannot be random. The Mplus model offers users a choice of treating time scores as data or parameters and of having random or fixed slopes for time-varying covariates.
The Mplus User's Guide has many examples. Some have references. All of these examples and Monte Carlo counterparts of most are available on the website and also come with the Mplus CD. Some theoretical specifications can be found in the Technical Appendices which are also on the website. There are also many references on the website for the various methods. If you are interested in a particular type of modeling, for example, growth modeling, the references on the website should be helpful.