Modeling sign concordance of quantile regression residuals with multiple outcomes
Abstract
Quantile regression permits describing how quantiles of a scalar response variable depend on a set of predictors. Because a unique definition of multivariate quantiles is lacking, extending quantile regression to multivariate responses is somewhat complicated. In this paper, we describe a simple approach based on a two-step procedure: in the first step, quantile regression is applied to each response separately; in the second step, the joint distribution of the signs of the residuals is modeled through multinomial regression. The described approach does not require a multidimensional definition of quantiles, and can be used to capture important features of a multivariate response and assess the effects of covariates on the correlation structure. We apply the proposed method to analyze two different datasets.
Keywords
Cite
@article{arxiv.2104.10436,
title = {Modeling sign concordance of quantile regression residuals with multiple outcomes},
author = {Silvia Columbu and Paolo Frumento and Matteo Bottai},
journal= {arXiv preprint arXiv:2104.10436},
year = {2021}
}