Multivariate latent class profile analysis (MLCPA) is a useful tool for exploring the stage-sequential process of multiple latent class variables, but the inference can be challenging due to the high-dimensional latent structure of the model. In this paper, a Bayesian approach via Markov chain Monte Carlo (MCMC) is proposed for MLCPA as an alternative to the maximum-likelihood (ML) method. Compared to the ML solution, Bayesian estimates are less sensitive to the set of initial values as well as easier to obtain standard errors. We also address issues in MCMC such as label-switching problem with a dynamic data-dependent prior and computational complexity with a recursive formula. Simulation studies revealed the validity and efficiency of the proposed algorithm. An empirical analysis of MLCPA using the National Longitudinal Survey of Youth 97 (NLSY97) identified a small number of representative developmental progressions of adolescent depression and substance use.

多元潜在类概貌分析（MLCPA）是探索多个潜在类变量的阶段顺序过程的有用工具，但是由于模型的高维潜在结构，推断可能具有挑战性。本文提出了一种基于马尔可夫链蒙特卡罗（MCMC）的贝叶斯方法，作为MLCPA的一种替代方法，作为最大似然法（ML）的一种替代方法。与ML解决方案相比，贝叶斯估计对初始值集不那么敏感，并且更容易获得标准误差。我们还解决了MCMC中的问题，例如具有动态数据相关先验的标签交换问题以及具有递归公式的计算复杂性。仿真研究表明了该算法的有效性和有效性。