AStA Advances in Statistical Analysis

, Volume 103, Issue 4, pp 453–473 | Cite as

A joint quantile regression model for multiple longitudinal outcomes

  • Hemant Kulkarni
  • Jayabrata Biswas
  • Kiranmoy DasEmail author
Original Paper


Complexity of longitudinal data lies in the inherent dependence among measurements from same subject over different time points. For multiple longitudinal responses, the problem is challenging due to inter-trait and intra-trait dependence. While linear mixed models are popularly used for analysing such data, appropriate inference on the shape of the population cannot be drawn for non-normal data sets. We propose a linear mixed model for joint quantile regression of multiple longitudinal responses. We consider an asymmetric Laplace distribution for quantile regression and estimate model parameters by Monte Carlo EM algorithm. Nonparametric bootstrap resampling method is used for estimating confidence intervals of parameter estimates. Through extensive simulation studies, we investigate the operating characteristics of our proposed model and compare the performance to other traditional quantile regression models. We apply proposed model for analysing data from nutrition education programme on hypercholesterolemic children of the USA.


Asymmetric Laplace Distribution EM algorithm Longitudinal data MCMC Quantile regression 



The authors sincerely thank Prof. Vern Chinchilli, the Pennsylvania State University, for sharing data from one-year nutrition education.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Hemant Kulkarni
    • 1
  • Jayabrata Biswas
    • 2
  • Kiranmoy Das
    • 2
    Email author
  1. 1.Human Genetics UnitIndian Statistical InstituteKolkataIndia
  2. 2.Interdisciplinary Statistical Research UnitIndian Statistical InstituteKolkataIndia

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