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M-quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study

M-quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study
M-quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study
Motivated by the analysis of data from the UK Millennium Cohort Study on emotional and behavioural disorders, we develop an M-quantile regression model for multivariate longitudinal responses. M-quantile regression is an appealing alternative to standard regression models; it combines features of quantile and expectile regression and it may produce a detailed picture of the conditional response variable distribution, while ensuring robustness to outlying data. As we deal with multivariate data, we need to specify what it is meant by M-quantile in this context, and how the structure of dependence between univariate profiles may be accounted for. Here, we consider univariate (conditional) M-quantile regression models with outcome-specific random effects for each outcome. Dependence between outcomes is introduced by assuming that the random effects in the univariate models are dependent. The multivariate distribution of the random effects is left unspecified and estimated from the observed data. Adopting this approach, we are able to model dependence both within and between outcomes. We further discuss a suitable model parameterisation to account for potential endogeneity of the observed covariates. An extended EM algorithm is defined to derive estimates under a maximum likelihood approach.
0035-9254
122-146
Alfò, Marco
dad67665-30d4-4e5a-abc7-d1a9005bae7b
Marino, Francesca
89a6baa4-7a49-40e8-9caf-87514ff02204
Ranalli, Maria Giovanna
b5f1a69a-7b7d-4595-9db1-94428e7abe70
Salvati, Nicola
9be298e5-de55-4a24-9361-054a2ec09726
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Alfò, Marco
dad67665-30d4-4e5a-abc7-d1a9005bae7b
Marino, Francesca
89a6baa4-7a49-40e8-9caf-87514ff02204
Ranalli, Maria Giovanna
b5f1a69a-7b7d-4595-9db1-94428e7abe70
Salvati, Nicola
9be298e5-de55-4a24-9361-054a2ec09726
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a

Alfò, Marco, Marino, Francesca, Ranalli, Maria Giovanna, Salvati, Nicola and Tzavidis, Nikolaos (2020) M-quantile regression for multivariate longitudinal data with an application to the Millennium Cohort Study. Journal of the Royal Statistical Society: Series C (Applied Statistics), 70 (1), 122-146. (doi:10.1111/rssc.12452).

Record type: Article

Abstract

Motivated by the analysis of data from the UK Millennium Cohort Study on emotional and behavioural disorders, we develop an M-quantile regression model for multivariate longitudinal responses. M-quantile regression is an appealing alternative to standard regression models; it combines features of quantile and expectile regression and it may produce a detailed picture of the conditional response variable distribution, while ensuring robustness to outlying data. As we deal with multivariate data, we need to specify what it is meant by M-quantile in this context, and how the structure of dependence between univariate profiles may be accounted for. Here, we consider univariate (conditional) M-quantile regression models with outcome-specific random effects for each outcome. Dependence between outcomes is introduced by assuming that the random effects in the univariate models are dependent. The multivariate distribution of the random effects is left unspecified and estimated from the observed data. Adopting this approach, we are able to model dependence both within and between outcomes. We further discuss a suitable model parameterisation to account for potential endogeneity of the observed covariates. An extended EM algorithm is defined to derive estimates under a maximum likelihood approach.

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More information

Accepted/In Press date: 2 September 2020
e-pub ahead of print date: 25 November 2020

Identifiers

Local EPrints ID: 443832
URI: http://eprints.soton.ac.uk/id/eprint/443832
ISSN: 0035-9254
PURE UUID: 53378c6c-1ea2-4b09-8037-1d789d36dd04
ORCID for Nikolaos Tzavidis: ORCID iD orcid.org/0000-0002-8413-8095

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Date deposited: 14 Sep 2020 16:36
Last modified: 29 Jul 2022 04:02

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Contributors

Author: Marco Alfò
Author: Francesca Marino
Author: Maria Giovanna Ranalli
Author: Nicola Salvati

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