A time-varying latent variable model is proposed to jointly analyze multivariate mixed-support longitudinal data. The proposal can be viewed as an extension of hid- den Markov regression models with fixed covariates (HMRMFCs), that is the state of the art for modelling longitudinal data, with a special focus on the underlying clustering structure. HMRMFCs assume fixed covariates, and the modeling for the covariates is not considered. This aspect makes HMRMFCs inadequate for appli- cations in which a clustering structure can be identified in the distribution of the covariates, as the clustering is independent from the covariates distribution. Here, hidden Markov regression models with random covariates (HMRMRCs) are intro- duced by explicitly specifying state-specific distributions for the covariates, with the aim of improving the recovering of the clusters in the data with respect to a fixed covariates paradigm. The HMRMRCs class is defined focusing on the exponential family, in a generalized linear model framework. Model identifiability conditions are sketched, an expectation-maximization algorithm is outlined for parameter estima- tion, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients, as well as of the hidden path param- eters, are evaluated through simulation experiments, and compared with those of HMRMFCs. The method is applied to physical activity data.
|Titolo:||Multivariate generalized hidden Markov regression models with random covariates: physical exercise in an elderly population|
|Data di pubblicazione:||2018|
|Appare nelle tipologie:||1.1 Articolo in rivista|