This dissertation consists of two studies that introduce and investigate two Bayesian non/semi-parametric estimation methods for latent growth mixture modeling (LGMM). LGMM is a useful statistical tool for modeling latent classes or unobserved subgroups in longitudinal data analysis. One of the major challenges of fitting an LGMM is deciding on the number of latent classes that exist in the population from which data were collected. In this dissertation, I introduce two non/semi-parametric estimation methods, that is Reversible jump Markov chain Monte Carlo (RJMCMC) and Dirichlet process modeling (DP) for LGMM. Specifically, I examined the estimation performance of these two non/semi-parametric methods along with traditional estimation methods, such as maximum likelihood (ML) and the Bayesian estimation framework. I also investigated some commonly discussed topics within the LGMM context, such as class enumeration and the impact of class separation. In particular, Study 1 examines the ability of RJMCMC, DP, and ML to recover the model parameters, especially the number of classes and class sizes via a simulation study. Simulation results showed that RJMCMC and DP performed comparable to ML and even better under some conditions for some parameters. An empirical example is included in Study 1 as an illustration of how to apply RJMCMC and DP; the example uses an education-related data set and covers how to interpret the results. In Study 2, the investigation is focused on the impact of class separation on class enumeration and model parameter recovery. Specifically, different degrees of class separation and several separation conditions were investigated. The performance of RJMCMC, DP and two Bayesian estimation methods with different prior specifications were examined for the LGMM via a simulation study. Results of Study 2 showed that RJMCMC and DP performed comparable to the Bayesian estimators under different degrees of class separation. Findings of the two studies suggested that RJMCMC and DP can be used as alternatives to traditional ML and Bayesian estimation methods in accurately recovering the number of latent classes for LGMM under most conditions. However, there are added benefits to the use of RJMCMC and DP over the other approaches. Other implications, suggestions for applied researchers, limitations, and future directions are also discussed.

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