Galarza, Christian E.; Lachos, Victor H.; Bandyopadhyay, Dipankar Quantile regression in linear mixed models: a stochastic approximation EM approach. (English) Zbl 1388.62201 Stat. Interface 10, No. 3, 471-482 (2017). Summary: This paper develops a likelihood-based approach to analyze quantile regression (QR) models for continuous longitudinal data via the asymmetric Laplace distribution (ALD). Compared to the conventional mean regression approach, QR can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. Exploiting the nice hierarchical representation of the ALD, our classical approach follows a stochastic approximation of the EM (SAEM) algorithm in deriving exact maximum likelihood estimates of the fixed-effects and variance components. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to two real life datasets. Our empirical results clearly indicate that the SAEM estimates outperforms the estimates obtained via the combination of Gaussian quadrature and non-smooth optimization routines of the approach of M. Geraci and M. Bottai [Stat. Comput. 24, No. 3, 461–479 (2014; Zbl 1325.62010)] in terms of standard errors and mean square error. The proposed SAEM algorithm is implemented in the \(\mathsf{R}\) package \(\mathsf{qrLMM()}\). Cited in 1 ReviewCited in 5 Documents MSC: 62J02 General nonlinear regression 62L20 Stochastic approximation 62F12 Asymptotic properties of parametric estimators 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:asymmetric Laplace distribution; SAEM algorithm; likelihood Citations:Zbl 1325.62010 Software:qrLMM; R PDFBibTeX XMLCite \textit{C. E. Galarza} et al., Stat. Interface 10, No. 3, 471--482 (2017; Zbl 1388.62201) Full Text: DOI