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We present a flexible Bayesian semiparametric mixed model for longitudinaldata analysis in the presence of potentially high-dimensional categoricalcovariates. Building on a novel hidden Markov tensor decomposition technique,our proposed method allows the fixed effects components to vary betweendependent random partitions of the covariate space at different time points.The mechanism not only allows different sets of covariates to be included inthe model at different time points but also allows the selected predictors'influences to vary flexibly over time. Smooth time-varying additive randomeffects are used to capture subject specific heterogeneity. We establishposterior convergence guarantees for both function estimation and variableselection. We design a Markov chain Monte Carlo algorithm for posteriorcomputation. We evaluate the method's empirical performances through syntheticexperiments and demonstrate its practical utility through real worldapplications.

Bayesian Semiparametric Hidden Markov Tensor Partition Models for Longitudinal Data with Local Variable Selection