I am relatively new to mPlus and still feeling my way around but I already have a question about what seems to me to be a fairly complex model that fits somewhere within growth mixture modeling (GMM), latent transition analysis (LTA), and modeling parallel processes. Here is the conceptual issue:
I have a longitudinal data set with up to 43 different time points (semi-annual measurements) for a group of about 4,000 individuals. I want to model their HIV risk behavior defined over time. In this instance, I want to develop the measure using item response theory analyses first to obtain a continuous, repeated measure for HIV risk.
I am then interested in relating this continuous repeated measure to substance use, which cross-sectional analyses tells me can be represented by 4 latent classes.
The analytic problem is that I expect both substance use latent class as well as HIV risk to vary over time and I want to capture both their variations and covariations over time but how? It seems the best way to capture variation in HIV risk is to do LCGA or GMM and the best way to capture variation in substance use is to use LTA. But can these two techniques be combined to show how the time-varying pattern of substance use affects the time-varying pattern of HIV risk?
In addition, I have another variable, the advent of Highly Active Antiretroviral Treatment (HAART) in 1997, which may have actually increased HIV risk and substance use post 1997. So I am interested in comparing the patterns of risk and substance use pre and post the introduction of HAART to see if, in fact, it made matters worse in some ways. A person's change in HIV status (i.e., they become positive, may also affect both processes).
In the non-latent world, modeling the effect of the onset of HAART might have been captured with regression discontinuity analyses. How would I include this factor in the above latent variable longitudinal model, along with HIV status as a time varying covariate whatever that might be?
Guidance on any examples of similar work (not substantively but statistically) using mPlus or in publications would be much appreciated. Sorry if this is redundant with other information already posted on the board.
Just a correction, I did not mean to imply in my above post that I did not know what a time varying covariate is.... I meant the phrase "whatever that might be" to refer to the overall latent variable model with the continuous and categorical latent variables.
Mplus can handle a latent transition model together with a growth model, where the latent classes of the LTA influence the growth model. And the pre- and post-treatment periods can be given different parameter values via piecewise growth modeling and different parameter values pre and post in the LTA. I have not seen any writings on this kind of modeling - it takes an experienced Mplus modeler.
I thought of one paper that is somewhat related - the one by Boscardin et al under Growth Mixture Modeling in the Papers section. One of the models is an LTA for 2 time segments (Kindergarten vs 1st-2nd grade) where the LTA "outcomes" are the latent growth factors.
I am also relatively new in working with MPlus en was having some doubts about a rather complicated research question that could be similar to the one asked above. Specifically, we are interested in finding out if students' changes from one track to another in secondary education (with associated differences in the mean achievement level surrounding the student) are associated with similar changes in students' academic self-concept. For example, if a student moves to a lower achieving track, his or her self-concept might enhance following this transition. We are mainly interested in the effect of three existing global tracks. A colleague told me it would be best to use latent transition analysis, would you agree? Or would another type of analysis be better?
Another possibility is a parallel process growth model with one process for achievement and the other for self-concept using status change as a time-varying covariate. See the short course handout for Topic 3 starting at slide 155 for an example of time-varying covariates representing status change.
I did something very similar to what you are interested in modeling for my dissertation. Specifically, I modeled the growth of risk behaviors in concert with the growth in cognitive processing. Here's a link to my dissertation if you're interested in seeing what I did: