Parametric modeling of quantile regression coefficient functions with longitudinal data
Fernandez-Val, Ivan; Frumento, Paolo; Bottai, Matteo
In 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.
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