Hidden Markov models (HMMs), which can characterize dynamic heterogeneity, are valuable tools for analyzing longitudinal data. The order of HMMs (ie, the number of hidden states) is typically assumed to be known or predetermined by some model selection criterion in conventional analysis. As prior information about the order frequently lacks, pairwise comparisons under criterion-based methods become computationally expensive with the model space growing. A few studies have conducted order selection and parameter estimation simultaneously, but they only considered homogeneous parametric instances. This study proposes a Bayesian double penalization (BDP) procedure for simultaneous order selection and parameter estimation of heterogeneous semiparametric HMMs. To overcome the difficulties in updating the order, we create a brand-new Markov chain Monte Carlo algorithm coupled with an effective adjust-bound reversible jump strategy. Simulation results reveal that the proposed BDP procedure performs well in estimation and works noticeably better than the conventional criterion-based approaches. Application of the suggested method to the Alzheimer's Disease Neuroimaging Initiative research further supports its usefulness.
Keywords: Bayesian method; double penalization; dynamic heterogeneity; longitudinal data; semiparametric model.
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