Quantile regression for longitudinal data

Authors:
Roger Koenker
Affiliations:
Department of Economics, University of Illinois at Urbana-Champaign, Boy 111-1206 South-Sixth St., Champaign, IL
Venue:
Journal of Multivariate Analysis - Special issue on semiparametric and nonparametric mixed models
Year:
2004

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Abstract

The penalized least squares interpretation of the classical random effects estimator suggests a possible way forward for quantile regression models with a large number of "fixed effects". The introduction of a large number of individual fixed effects can significantly inflate the variability of estimates of other covariate effects. Regularization, or shrinkage of these individual effects toward a common value can help to modify this inflation effect. A general approach to estimating quantile regression models for longitudinal data is proposed employing l1 regularization methods. Sparse linear algebra and interior point methods for solving large linear programs are essential computational tools.