Fernandez-Val, IvanFrumento, PaoloBottai, Matteo2021-03-232021-03-232020Ivan Fernandez-Val, Paolo Frumento, Matteo Bottai. "Parametric Modeling of Quantile Regression Coefficient Functions with Longitudinal Data." Journal of the American Statistical Association, https://arxiv.org/abs/2006.00160v10162-1459https://hdl.handle.net/2144/42306In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (qrcm), is to model quantile regression coefficients as parametric functions of the order of the quantile. In this paper, we describe how the qrcm paradigm can be applied to longitudinal data. We introduce a two-level quantile function, in which two different quantile regression models are used to describe the (conditional) distribution of the within-subject response and that of the individual effects. We propose a novel type of penalized fixed-effects estimator, and discuss its advantages over standard methods based on ℓ1 and ℓ2 penalization. We provide model identifiability conditions, derive asymptotic properties, describe goodness-of-fit measures and model selection criteria, present simulation results, and discuss an application. The proposed method has been implemented in the R package qrcm.en-USStatisticsEconometricsDemographyStatistics & probabilityLongitudinal quantile regressionTwo-level quantile functionParametric quantile functionPenalized fixed-effectsR package qrcmArticle590616