How can the order of heterogeneous hidden Markov models (HMMs) be efficiently selected for analyzing longitudinal data? This study introduces a Bayesian double penalization (BDP) procedure for simultaneous order selection and parameter estimation in heterogeneous semiparametric HMMs. HMMs are valuable tools for characterizing dynamic heterogeneity in data. To overcome the challenges in updating the order, the researchers developed a novel Markov chain Monte Carlo algorithm coupled with an effective adjust-bound reversible jump strategy. This algorithm facilitates estimation and improves upon conventional criterion-based approaches. Through simulation results, the proposed BDP procedure demonstrates strong performance in estimation. The application of this method to the Alzheimer's Disease Neuroimaging Initiative research further supports its usefulness. This study advances the analysis of longitudinal data by providing a robust and efficient method for order selection in HMMs.
Published in Statistics in Medicine, which addresses the development and application of statistical methods in health and medical research, this study introduces a novel statistical procedure applicable to medical data. By focusing on Alzheimer's Disease Neuroimaging Initiative data, the paper demonstrates its relevance to analyzing complex longitudinal datasets in medical research, aligning with the journal's scope.