Multivariate Mixed Hidden Markov Model for joint estimation of multiple quantiles

This paper develops a Mixed Hidden Markov Model for joint estimation of multiple quantiles in a multivariate linear regression for longitudinal data. This method accounts for association among multiple responses and study how the relationship between dependent and explanatory variables may vary across different quantile levels of the conditional distribution of the multivariate response variable. Unobserved heterogeneity sources and serial dependence are jointly modeled through the introduction of individual-specific, time-constant random coefficients and time-varying parameters that evolve over time with a Markovian structure, respectively. Estimation is carried out via a suitable EM algorithm without parametric assumptions on the random effects distribution. We assess the empirical behaviour of the proposed methodology through the analysis of the Millennium Cohort Study data.