Title: M-quantile regression for multivariate longitudinal data
Authors: Maria Francesca Marino - University of Florence (Italy) [presenting]
Marco Alfo - University La Sapienza, Rome (Italy)
Maria Giovanna Ranalli - University of Perugia (Italy)
Nicola Salvati - University of Pisa (Italy)
Nikos Tzavidis - University of Southampton (United Kingdom)
Abstract: Recently, there has been an increasing interest in the analysis of longitudinal data via quantile and M-quantile regression with the aim of studying the effect of observed covariates at different levels of the response distribution. When compared to mean regression, such approaches offer a more complete picture of the response of interest. We propose a multivariate finite mixture of M-quantile regression models to deal with multivariate longitudinal responses. Discrete, individual-specific, random parameters are used to account for both dependence within the same response recorded at different time occasions and association between multiple responses observed on the same unit at a given time. The distribution of the random parameters is left unspecified and is directly estimated from the observed data. Furthermore, to account for potential endogeneity of observed covariates, we propose the definition of an auxiliary regression model. Within and between effects of time-varying covariates on the M-quantiles of the response distribution are separately modeled to avoid bias. An extended EM algorithm is proposed to derive parameter estimates under a maximum likelihood approach. The model is applied to the analysis of data from the millennium cohort study on children internalizing and externalizing disorders.