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We show that the estimating equations for quantile regression can be solvedusing a simple EM algorithm in which the M-step is computed via weighted leastsquares, with weights computed at the E-step as the expectation of independentgeneralized inverse-Gaussian variables. We compute the variance-covariancematrix for the quantile regression coefficients using a kernel densityestimator that results in more stable standard errors than those produced byexisting software. A natural modification of the EM algorithm that involvesfitting a linear mixed model at the M-step extends the methodology to mixedeffects quantile regression models. In this case, the fitting method can bejustified as a generalized alternating minimization algorithm. Obtainingquantile regression estimates via the weighted least squares method enablesmodel diagnostic techniques similar to the ones used in the linear regressionsetting. The computational approach is compared with existing software usingsimulated data, and the methodology is illustrated with several case studies.

Quantile Regression Modelling via Location and Scale Mixtures of Normal Distributions