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Title: Quantile mixed hidden Markov models for multivariate longitudinal data: An application to children's SDQ scores Authors:  Luca Merlo - European University of Rome (Italy) [presenting]
Lea Petrella - Sapienza University of Rome (Italy)
Nikos Tzavidis - University of Southampton (United Kingdom)
Abstract: The identification of factors associated with mental and behavioural disorders in early childhood is critical both for psychopathology research and the support of primary health care practices. Motivated by the Millennium Cohort Study, we study the effect of a comprehensive set of covariates on children's emotional and behavioural trajectories in England. To this end, we develop a quantile mixed hidden Markov model for joint estimation of multiple quantiles in a linear regression setting for multivariate longitudinal data. The novelty of the proposed approach is based on the multivariate asymmetric Laplace distribution, which allows us to jointly estimate the quantiles of the univariate conditional distributions of a multivariate response, accounting for possible correlation between the outcomes. Sources of unobserved heterogeneity and serial dependency due to repeated measures are modelled through the introduction of individual-specific, time-constant random coefficients and time-varying parameters evolving over time with a Markovian structure, respectively. The inferential approach is carried out through the construction of a suitable expectation-maximization algorithm without parametric assumptions on the random effects distribution.