A joint quantile regression model for multiple longitudinal outcomes

• Published in: Advances in statistical analysis : AStA : a journal of the German Statistical Society Vol. 103; no. 4; pp. 453 - 473
• Main Authors: Kulkarni, Hemant, Biswas, Jayabrata, Das, Kiranmoy
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2019; Springer Nature B.V
• Subjects: Algorithms; Computer simulation; Confidence intervals; Data analysis; Dependence; Econometrics; Economic models; Economics; Finance; Insurance; Management; Mathematics and Statistics; Nutrition; Original Paper; Parameter estimation; Probability Theory and Stochastic Processes; Regression analysis; Regression models; Resampling; Simulation; Skewed distributions; Statistical analysis; Statistics; Statistics for Business; MCMC; Asymmetric Laplace Distribution; Longitudinal data; Quantile regression; EM algorithm
• ISSN: 1863-8171; 1863-818X
• DOI: 10.1007/s10182-018-00339-9

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.