On a multivariate regression model for rates and proportions

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 SB class of distributions. In this paper we generalize this class of univariate distributions to the multivariate case whose marginals are SB 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.