Bayesian Analysis for Mixture of Latent Variable Hidden Markov Models with Multivariate Longitudinal data

Latent variable hidden Markov models (LVHMMs) are important statistical methods in exploring the possible heterogeneity of data and explaining the pattern of subjects moving from one group to another over time. Classic subject- and/or time-homogeneous assumptions on transition matrices in transition model as well as the emission distribution in the observed process may be inappropriate to interpret heterogeneity at the subject level. For this end, a general extension of LVHMM is proposed to address the heterogeneity of multivariate longitudinal data both at the subject level and the occasion level. The main modeling strategy is that the observed time sequences are first grouped into different clusters, and then within each cluster the observed sequences are formulated via latent variable hidden Markov model. The local heterogeneity at the occasion level is characterized by the distribution related to the latent states, while the global heterogeneity at the subject level is identified with the finite mixture model. Compared to the existing methods, an appeal underlying the proposal is its capacity of accommodating non-homogeneous patterns of state sequences and emission distributions across the subjects simultaneously. As a result, the proposal provides a comprehensive framework for exploring various kinds of relevance among the multivariate longitudinal data. Within the Bayesian paradigm, Markov Chains Monte Carlo (MCMC) method is used to implement posterior analysis. Gibbs sampler is used to draw observations from the related full conditionals and posterior inferences are carried out based on these simulated observations. Empirical results including simulation studies and a real example are used to illustrate the proposed methodology

潜在变量隐马尔可夫模型（LVHMMs）是探索数据可能的异质性以及解释个体随时间从一个组转移到另一个组的模式的重要统计方法。转移模型中对转移矩阵以及观测过程中的发射分布的经典的个体和/或时间同质性假设可能不适合解释个体层面的异质性。为此，提出了一种对LVHMM的通用扩展，以解决多变量纵向数据在个体层面和时点层面的异质性。主要的建模策略是，首先将观测到的时间序列分组到不同的簇中，然后在每个簇内通过潜在变量隐马尔可夫模型构建观测序列。时点层面的局部异质性由与潜在状态相关的分布来表征，而个体层面的全局异质性通过有限混合模型来识别。与现有方法相比，该方法的一个吸引人之处在于它能够同时适应个体间状态序列和发射分布的非同质模式。因此，该方法为探索多变量纵向数据之间的各种相关性提供了一个综合框架。在贝叶斯范式内，使用马尔可夫链蒙特卡罗（MCMC）方法进行后验分析。使用吉布斯采样器从相关的全条件分布中抽取观测值，并基于这些模拟观测值进行后验推断。包括模拟研究和一个实际例子在内的实证结果用于说明所提出的方法