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Modeling sign concordance of quantile regression residuals with multiple outcomes

Author

Listed:
  • Columbu Silvia

    (University of Cagliari, Cagliari, Italy)

  • Frumento Paolo

    (University of Pisa, Pisa, Italy)

  • Bottai Matteo

    (Karolinska Institute, Solna, Stockholm, Sweden)

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.

Suggested Citation

  • Columbu Silvia & Frumento Paolo & Bottai Matteo, 2023. "Modeling sign concordance of quantile regression residuals with multiple outcomes," The International Journal of Biostatistics, De Gruyter, vol. 19(1), pages 97-110, May.
    • Handle: RePEc:bpj:ijbist:v:19:y:2023:i:1:p:97-110:n:4
    DOI: 10.1515/ijb-2022-0020
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