Statistical Modelling 20 (4) (2020), 369–385
A penalized approach to covariate selection through quantile regression coefficient models
Gianluca Sottile,
Institute of Environmental Medicine,
Unit of Biostatistics,
Karolinska Institutet,
Stockholm,
Sweden.
e-mail: gianluca.sottile@unipa.it
Paolo Frumento,
Department of Economics,
Business and Statistics,
University of Palermo,
Palermo,
Italy.
Marcello Chiodi,
Department of Economics,
Business and Statistics,
University of Palermo,
Palermo,
Italy.
Matteo Bottai,
Institute of Environmental Medicine,
Unit of Biostatistics,
Karolinska Institutet,
Stockholm,
Sweden.
Abstract:
The coefficients of a quantile regression model are one-to-one functions of the order of the quantile. In standard quantile regression (QR), different quantiles are estimated one at a time. Another possibility is to model the coefficient functions parametrically, an approach that is referred to as quantile regression coefficients modeling (QRCM). Compared with standard QR, the QRCM approach facilitates estimation, inference and interpretation of the results, and generates more efficient estimators. We designed a penalized method that can address the selection of covariates in this particular modelling framework. Unlike standard penalized quantile regression estimators, in which model selection is quantile-specific, our approach permits using information on all quantiles simultaneously. We describe the estimator, provide simulation results and analyse the data that motivated the present article. The proposed approach is implemented in the qrcmNP package in R.
Keywords:
inspiratory capacity, Lasso penalty, Penalized integrated loss minimization (PILM), penalized quantile regression coefficients modelling (QRCMp), tuning parameter selection.
Downloads:
Example data and code in
zipped archive.
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