A new family of quantile regression models applied to nutritional data

Abstract

This paper introduces a new family of quantile regression models whose response variable follows a reparameterized Marshall-Olkin distribution indexed by quantile, scale, and asymmetry parameters. The family has arisen by applying the Marshall-Olkin approach to distributions belonging to the location-scale family. Models of higher flexibility and whose structure is similar to generalized linear models were generated by quantile reparameterization. The maximum likelihood (ML) method is presented for the estimation of the model parameters, and simulation studies evaluated the performance of the ML estimators. The advantages of the family are illustrated through an application to a set of nutritional data, whose results indicate it is a good alternative for modeling slightly asymmetric response variables with support on the real line.

Keywords:

• Quantile regression
• asymmetric distributions
• diagnostic analysis
• local influence
• nutritional data

Acknowledgments

The authors acknowledge the editors and reviewers for their constructive comments on an earlier version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was partially financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior–Brasil (CAPES)–Finance Code 001 and M. de Castro's research is partially funded by CNPq (Grant number 304904/2020-1), Brazil.