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Quantile mixed hidden Markov models for multivariate longitudinal data: An application to children's Strengths and Difficulties Questionnaire scores

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  • Luca Merlo
  • Lea Petrella
  • Nikos Tzavidis

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, in this paper 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 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.

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  • Luca Merlo & Lea Petrella & Nikos Tzavidis, 2022. "Quantile mixed hidden Markov models for multivariate longitudinal data: An application to children's Strengths and Difficulties Questionnaire scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 417-448, March.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:2:p:417-448
    DOI: 10.1111/rssc.12539
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    Cited by:

    1. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    2. Valeria Bignozzi & Luca Merlo & Lea Petrella, 2022. "Inter-order relations between moments of a Student $t$ distribution, with an application to $L_p$-quantiles," Papers 2209.12855, arXiv.org.

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