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Bayesian non-parametric (BNP) modeling has been developed and proven to be a powerful tool to analyze messy data with complex structures. Despite the increasing popularity of BNP modeling, it also faces challenges. One challenge is the estimation of the precision parameter in the Dirichlet process mixtures. In this study, we focus on a BNP growth curve model and investigate how non-informative prior, weakly informative prior, accurate informative prior, and inaccurate informative prior affect the model convergence, parameter estimation, and computation time. A simulation study has been conducted. We conclude that the non-informative prior for the precision parameter is less preferred because it yields a much lower convergence rate, and growth curve parameter estimates are not sensitive to informative priors. 

Growth mixture modeling is a popular analytic tool for longitudinal data analysis. It detects latent groups based on the shapes of growth trajectories. Traditional growth mixture modeling assumes that outcome variables are normally distributed within each class. When data violate this normality assumption, however, it is well documented that the traditional growth mixture modeling mislead researchers in determining the number of latent classes as well as in estimating parameters. To address nonnormal data in growth mixture modeling, robust methods based on various nonnormal distributions have been developed. As a new robust approach, growth mixture modeling based on conditional medians has been proposed. In this article, we present the results of two simulation studies that evaluate the performance of the median-based growth mixture modeling in identifying the correct number of latent classes when data follow the normality assumption or have outliers. We also compared the performance of the median-based growth mixture modeling to the performance of traditional growth mixture modeling as well as robust growth mixture modeling based on t distributions. For identifying the number of latent classes in growth mixture modeling, the following three Bayesian model comparison criteria were considered: deviance information criterion, Watanabe-Akaike information criterion, and leave-one-out cross validation. For the median-based growth mixture modeling and t -based growth mixture modeling, our results showed that they maintained quite high model selection accuracy across all conditions in this study (ranged from 87 to 100%). In the traditional growth mixture modeling, however, the model selection accuracy was greatly influenced by the proportion of outliers. When sample size was 500 and the proportion of outliers was 0.05, the correct model was preferred in about 90% of the replications, but the percentage dropped to about 40% as the proportion of outliers increased to 0.15.