What Problems am I Likely to Encounter?
We have encountered many choice points and challenges in our application of RMLCA to smoking data. You will need to make key decisions about what observed indicators to use, how to code them, and what level of precision and scale of time you wish to examine.
You will also have to consider potential model identification problems and the possibility that you will find a solution that is a locally optimized but not fully optimized solution (i.e., that your model results are not consistent across a wide range of starting values). This problem may indicate that your models are too complex (in terms of levels of indicators or number of classes) or you do not have sufficient information (data) to estimate the unknowns in your model. We routinely run our models with 1000 starting values to identify this problem and simplify our models when this occurs.
Another critical and challenging choice point is deciding on the number of latent classes to retain. This decision is complex and should be informed by many factors, including conceptual considerations and fit indices. We prioritized conceptual considerations over small improvements in fit indices for our RMLCA of daily smoking status. We preferred a five-class solution to six- or seven-class solutions because the additional classes had low prevalence, were poorly differentiated from other classes in terms of daily smoking probabilities, and were highly similar to existing classes in terms of covariate relations and distal outcomes.
It is also possible that your latent class solution will change when you introduce covariates into the model. Ideally, this change is small, but it can sometimes be substantial. Substantial changes in the class solution and item response probabilities within classes that occur with the introduction of covariates may indicate that the latent class solution is not consistent across levels of the covariate. For example, it may be that changes to the latent class solution that occur when gender is introduced as a covariate indicate that there is a different latent class structure for men and women. A between groups analysis would allow exploration of differences in the latent class structure across men and women.
This is a relatively new technique, at least in its application to the study of relapse and examination of treatment effects. As such, it can be challenging to present the information as thoroughly as needed for editors, reviewers, and general readers within the page or word limitations of journals. It can also be quite challenging to convey the meaning of complex associations between covariates and latent class membership, as the covariate relations are captured in terms of association with particular contrasts between latent classes (e.g., how is gender associated with the odds of being in a tobacco abstainer-class versus a continuing smoker class).