Multivariate generalized hidden Markov regression models with random covariates: Physical exercise in an elderly...

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Current hidden Markov regression models with fixed covariates (HMRMFCs) struggle with clustering structures dependent on covariate distributions.
• Existing models do not adequately capture the interplay between clustering and covariate distributions in longitudinal data.

Purpose of the Study:

• To propose a novel time-varying latent variable model for multivariate mixed-support longitudinal data.
• To enhance the recovery of underlying data clusters by explicitly modeling state-specific covariate distributions.
• To extend the capabilities of hidden Markov regression models for complex longitudinal data structures.

Main Methods:

• Development of hidden Markov regression models with random covariates (HMRCs).
• Specification of state-specific distributions within an exponential family, generalized linear model framework.
• Utilizing an expectation-maximization algorithm for parameter estimation and discussing implementation issues.

Main Results:

• The proposed HMRCs model demonstrates improved cluster recovery compared to HMRMFCs.
• Simulation experiments evaluate the properties of regression coefficients and hidden path parameters.
• The method is successfully applied to analyze physical activity data.

Conclusions:

• The novel HMRCs framework offers a more robust approach for analyzing longitudinal data with inherent clustering.
• This model advances the state-of-the-art in statistical modeling for complex, mixed-support longitudinal datasets.
• The findings have implications for analyzing real-world data, such as physical activity patterns.