Inference on Quantile Regression for Heteroscedastic Mixed Models

This paper develops two weighted quantile rank score tests for the significance of fixed effects in a class of mixed models with nonhomogeneous groups. One test is constructed by weighting the residuals to account for heteroscedasticity, while the other test is based on asymptotically optimal weights accounting for both heteroscedasticity and correlation. Without appropriate weights to account for heteroscedasticity, the quantile rank score tests often perform poorly. In finite samples, the test with optimal weights tends to provide marginal improvement over the one with simpler weights unless the intra-subject correlation is extremely high. The proposed methods are useful to accommodate nonparametric error distributions in studying the effect of covariates on any conditional quantile of the response distribution. We illustrate the value of the proposed methods by modeling several quantiles of the apnea duration of the elderly during normal swallowing. Our method suggests significant interaction effect between feeding type and viscosity in the upper quantiles of the apnea distribution, a result that tends to be overlooked by usual linear mixed model approaches.