Modeling sign concordance of quantile regression residuals with multiple outcomes

Int J Biostat. 2022 Jul 11;19(1):97-110. doi: 10.1515/ijb-2022-0020. eCollection 2023 May 1.

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: conditional correlation; multinomial model; multiple quantiles; multivariate regression; sign-concordance.