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

Abstract

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 hidden Markov regression models with fixed covariates (HMRMFCs), which is the state of the art for modelling longitudinal data, with a special focus on the underlying clustering structure. HMRMFCs are inadequate for applications 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 are introduced 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 hidden Markov regression models with random covariates 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 estimation, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients, as well as of the hidden path parameters, are evaluated through simulation experiments and compared with those of HMRMFCs. The method is applied to physical activity data.

Initialization of Hidden Markov and Semi‐Markov Models: A Critical Evaluation of Several Strategies

“…Hidden (semi)-Markov models are the state of the art for modeling univariate and multivariate time series data (Barbu & Limnios, 2009;Bulla et al, 2010;Yu, 2010;Maruotti, 2011;Bartolucci et al, 2013;Zucchini et al, 2016). Applications can be found in ecology (Bulla et al, 2012;Martinez-Zarzoso & Maruotti, 2013;Mastrantonio et al, 2015;Maruotti et al, 2016Patterson et al, 2017), medicine (Shirley et al, 2010;Maruotti & Rocci, 2012;Langrock et al, 2013;Lagona et al, 2014;Marino et al, 2018;Punzo et al, 2018;2019), finance (Bulla & Bulla, 2006;Bulla, 2011;Ang & Timmermann, 2012;Langrock et al, 2012;Bernardi et al, 2017;Hambuckers et al, 2018;, psychology (Visser, 2011), social sciences (Langrock, 2011;Punzo & M & P Maruotti, 2016;, sport performance (Ötting et al, 2020), speech recognition (Khorram et al, 2015), music modelling (Pikrakis et al, 2006), network performance (Nguyen & Roughan, 2012) and in many more empirical settings (see Yu, 2015, and references therein).…”

A copula-based multivariate hidden Markov model for modelling momentum in football

“…However, as this assumption would here clearly be inadequate given that we consider count data, for the vector of observations mt in the baseline model formulation, we assume that the joint probability is obtained by the product of the marginal distributions, with K = 2 here. This assumption, also known as contemporaneous conditional independence, is often used in practice (see, for example, Wall and Li 2009;DeRuiter et al 2017;Punzo et al 2018;van Beest et al 2019). Taking the product of the marginal distributions is straightforward and allows a flexible choice of the marginals f (y mtk | s mt ) , k = 1, … , K .…”

A copula-based multivariate hidden Markov model for modelling momentum in football

“…with K = 2 here. This assumption (also known as contemporaneous conditional independence) is often used in practice (see, e.g., Wall and Li, 2009;DeRuiter et al, 2017;Punzo et al, 2018;van Beest et al, 2019). In Eq.…”