We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed method allows the fixed effects components to vary between dependent random partitions of the covariate space at different time points. The mechanism not only allows different sets of covariates to be included in the model at different time points but also allows the selected predictors' influences to vary flexibly over time. Smooth time-varying additive random effects are used to capture subject specific heterogeneity. We establish posterior convergence guarantees for both function estimation and variable selection. We design a Markov chain Monte Carlo algorithm for posterior computation. We evaluate the method's empirical performances through synthetic experiments and demonstrate its practical utility through real world applications.
翻译:在可能具有高维绝对共变状态的情况下,我们为纵向数据分析提出了一个灵活的贝叶斯半参数混合模型。基于一种新的隐蔽的Markov Exor分解技术,我们建议的方法允许固定效应组成部分在不同时间点的共变空间的依附随机分割之间有所差异。这一机制不仅允许在不同时间点将不同的一组共变变量纳入模型,还允许选定的预测者的影响随时间变化而变化。使用平滑的时间变化添加随机效应来捕捉特定对象的异质性。我们为功能估计和变量选择建立了后端趋同保证。我们设计了一个用于后端计算的Markov Monte Carlo算法链。我们通过合成实验来评估该方法的经验性表现,并通过现实世界应用来展示其实际效用。