| The traditional inference for the linear mixed models depends strongly on the normality assumption, which is easily violated in some applications. We develop a robust rank score test for linear quantile models with a random effect. The rank score test can be carried out at a single quantile level or jointly at several quantile levels. It is derived for homoscedastic error models, but is valid for inference on treatment effects in an important class of mixed models with heteroscedastic errors.;The proposed test is motivated by studies of GeneChip data to identify differentially expressed genes through the analysis of probe level measurements. Realizing that the number of replicates is usually small in GeneChip studies, we propose a genome-wide adjustment to the test statistic to account for within-array correlation and several enhanced quantile approaches by borrowing information across genes. Our empirical studies of GeneChip data show that inference on the quartiles of the gene expression distribution is a valuable complement to the usual mixed model analysis based on Gaussian likelihood. |
