Quantile crossing as it pertains to sample size and goodness of fit: A simulation study

Abstract

Estimation of quantile regression curves individually causes quantile crossing, which eventually leads to an invalid estimation of the predictor effect. This work implemented quantile regression coefficient modeling (QRCM) where the regression coefficients are modeled as parametric functions of the order of the quantile in other to eliminate crossing. Four different samples of sizes 30, 50, 100 and 500 were simulated in other to investigate the effect of sample size on crossing and also to investigate the effect of crossing on model fit. The results show that as the sample sizes were increased crossing was reduced, but with a very large sample size crossing was not observed at all. The results also revealed that the presence of crossing caused the models not to be well specified but with the elimination of crossing the models were seen to be well specified.