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We propose a M-quantile regression model for the analysis of multivariate,continuous, longitudinal data. M-quantile regression represents an appealingalternative to standard regression models, as it combines the robustness ofquantile and the efficiency of expectile regression, providing a completepicture of the response variable distribution. Discrete, individual-specific,random parameters are used to account for both dependence within the sameresponse recorded at different times and association between differentresponses observed on the same sample unit at a given time. A suitableparametrisation is also introduced in the linear predictor to account forpossible dependence between the individual specific random parameters and thevector of observed covariates, that is to account for endogeneity of somecovariates. An extended EM algorithm is proposed to derive model parameterestimates under a maximum likelihood approach. The model is applied to theanalysis of the strengths and difficulties questionnaire scores from theMillennium Cohort Study in the UK.

M-quantile regression for multivariate longitudinal data: analysis of the Millennium Cohort Study data