Letter to the Editor

Abstract

Galarza, Lachos and Bandyopadhyay (2017) have recently proposed a method of estimating linear quantile mixed models (Geraci and Bottai, 2014) based on a Monte Carlo EM algorithm. They assert that their procedure represents an improvement over the numerical quadrature and non-smooth optimization approach implemented by Geraci (2014). The objective of this note is to demonstrate that this claim is incorrect. We also point out several inaccuracies and shortcomings in their paper which affect other results and conclusions that can be drawn.

Figure 1.

Absolute values of bias for linear quantile mixed effects estimators based on quadrature & non-smooth optimization (filled circles) and approximated EM (filled triangles): β_τ,0 (upper left panels), β_τ,1 (upper right panels), β_τ,2 (lower left panels), and σ_τ (lower right panels).

Figure 2.

Root mean squared error (RMSE) for linear quantile mixed effects estimators based on quadrature & non-smooth optimization (filled circles) and approximated EM (filled triangles): β_τ,0 (upper left panels), β_τ,1 (upper right panels), β_τ,2 (lower left panels), and σ_τ (lower right panels). The RMSE values reported by Galarza et al. [1, Table 2] for the approximated EM are marked with empty triangles.