Quantile Mixed Hidden Markov Models for multivariate longitudinal data

TL;DR

This paper introduces a novel Quantile Mixed Hidden Markov Model for analyzing multivariate longitudinal data, capturing complex dependencies and heterogeneity in children's behavioral trajectories.

Contribution

It develops a new joint quantile estimation method using the Multivariate Asymmetric Laplace distribution with an EM algorithm, accounting for correlation and heterogeneity.

Findings

Effective modeling of children's behavioral trajectories.

Joint estimation of multiple quantiles improves understanding.

Handles correlation and heterogeneity without parametric assumptions.

Abstract

The identification of factors associated with mental and behavioral 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 modeled 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.