  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.
