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arXiv · 2104.10436

Modeling sign concordance of quantile regression residuals with multiple outcomes

Silvia Columbu·Paolo Frumento·Matteo Bottai
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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.

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Silvia Columbu, Paolo Frumento, Matteo Bottai. 2021-04-21. Modeling sign concordance of quantile regression residuals with multiple outcomes. https://arxiv.org/abs/2104.10436

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