On a multivariate regression model for rates and proportions

ABSTRACT

The paper by Johnson [Systems of frequency curves generated by the methods of translation, Biometrika 36 (2014), pp. 149–176] has introduced a very interesting univariate distribution with bounded support which is known in the statistical literature as the $S_B$ class of distributions. In this paper we generalize this class of univariate distributions to the multivariate case whose marginals are $S_B$ distributions. On the basis of the multivariate distribution introduced, we propose a multivariate regression model for dealing with multivariate response variables which are vectors of rates or proportions. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. Monte Carlo simulation results reveal that the maximum likelihood method can be used effectively in estimating the model parameters. An application to real data is presented to show the usefulness of the multivariate regression model in practice.

KEYWORDS:

• Likelihood-based inference
• multivariate Johnson distribution
• proportions
• rates

Acknowledgments

We deeply thank the Associate Editor and two anonymous referees for the valuable comments and suggestions which have improved considerably the first version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. In the statistical literature this type of data are known as compositional data [1].

Additional information

Funding

Artur Lemonte gratefully acknowledges the financial support of the Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) (grant 301808/2016–3). Germán Moreno–Arenas gratefully acknowledges grants from Mobility Program of the Universidad Industrial de Santander (Colombia).