Modelling and estimation of nonlinear quantile regression with clustered data

In regression applications, the presence of nonlinearity and correlation among observa-tionsoffercomputationalchallengesnotonlyintraditionalsettingssuchasleastsquaresregression, but also (and especially) when the objective function is nonsmooth as in thecase of quantile regression. Methods are developed for the modelling and estimation ofnonlinearconditionalquantilefunctionswhendataareclusteredwithintwo levelnesteddesigns.TheproposedestimationalgorithmisablendofasmoothingalgorithmforquantileregressionandasecondorderLaplacianapproximationfornonlinearmixedmodels.Thisoptimization approach has the appealing advantage of reducing the original nonsmoothproblemtoanapproximatedL2problem.Whiletheestimationalgorithmisiterative,theobjectivefunctiontobeoptimizedhasasimpleanalyticform.Theproposedmethodsareassessed through a simulation study and two applications, one in pharmacokinetics andonerelatedtogrowthcurvemodellinginagriculture