Conditional median-based Bayesian growth mixture modeling for nonnormal data

Growth mixture modeling is a common tool for longitudinal data analysis. One of the key assumptions of traditional growth mixture modeling is that repeated measures within each class are normally distributed. When this normality assumption is violated, traditional growth mixture modeling may provide misleading model estimation results and suffer from nonconvergence. In this article, we propose a robust approach to growth mixture modeling based on conditional medians and use Bayesian methods for model estimation and inferences. A simulation study is conducted to evaluate the performance of this approach. It is found that the new approach has a higher convergence rate and less biased parameter estimation than the traditional growth mixture modeling approach when data are skewed or have outliers. An empirical data analysis is also provided to illustrate how the proposed method can be applied in practice.