Extensions of latent class trajectory models

The latent variable model is a useful tool for longitudinal/multivariate data analysis. It not only deals with the trajectory of the entire response profile together, but also summarizes both continuous and categorical outcomes that may not be combined in a straightforward way. As a categorical latent variable model, the latent class model also classifies subjects according to their underlying heterogeneity and thus may facilitate further subgroup analysis if necessary.; This dissertation extends the existing latent class model methodology to two directions and applies them to a longitudinal psychiatric dataset. The first project, driven by the limited identifiability of the between level latent class in multilevel modeling, explores the possibility of a nested latent class model by reversing the conventional conditional order between the two levels. Although the straightforward interpretation of the between level class no longer holds in this identifiability-driven approach, we can still gain meaningful clinical implications from the association between the two levels of latent classes.; The second and third projects employ a shared parameter model to assess the impact of drop-out under the non-ignorable assumption. The second project models continuous longitudinal responses while the third binary. The non-ignorable drop-out of the longitudinal responses are confirmed in both projects, but the impacts of the drop-out differ in degree in terms of the significance change of model covariates. We propose that the difference is caused by loss of information due to changing the continuous outcome to the binary outcome.; All three projects employ a quasi-Newton algorithm to maximize the finite mixture likelihood function generated by the latent classes. Simulation studies have been performed to assess validity of the algorithm for all three estimations. The most dominant challenge in the latent class model is identifiability. In addition to the problems mentioned above, limited identifiability also imposes difficulties in various model diagnosis and assessment approaches.