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

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

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.

EM algorithm, finite mixtures, multivariate asymmetric Laplace distribution, non-parametric maximum likelihood, quantile regression, random effects model
0035-9254
417-448
Merlo, Luca
436fb4df-938c-4b5d-aedc-d68e85390a36
Petrella, Lea
bf351458-2a5a-452e-be73-496a19c4060a
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Merlo, Luca
436fb4df-938c-4b5d-aedc-d68e85390a36
Petrella, Lea
bf351458-2a5a-452e-be73-496a19c4060a
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a

Merlo, Luca, Petrella, Lea and Tzavidis, Nikolaos (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 (Applied Statistics), 71 (2), 417-448. (doi:10.1111/rssc.12539).

Record type: Article

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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Royal Stata Society Series C - 2022 - Merlo - Quantile mixed hidden Markov models for multivariate longitudinal data An - Version of Record
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Accepted/In Press date: 9 December 2021
e-pub ahead of print date: 22 January 2022
Published date: March 2022
Keywords: EM algorithm, finite mixtures, multivariate asymmetric Laplace distribution, non-parametric maximum likelihood, quantile regression, random effects model

Identifiers

Local EPrints ID: 454432
URI: http://eprints.soton.ac.uk/id/eprint/454432
ISSN: 0035-9254
PURE UUID: 5c400a89-8a77-4015-be99-8f7b668d3887
ORCID for Nikolaos Tzavidis: ORCID iD orcid.org/0000-0002-8413-8095

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Date deposited: 09 Feb 2022 17:38
Last modified: 17 Mar 2024 02:54

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Contributors

Author: Luca Merlo
Author: Lea Petrella

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