A general and unified parameterization of the beta distribution: A flexible and robust beta regression model

The beta regression model is a commonly used approach for modeling data in the unit intervals, such as rates, ratios, percentages, or proportions. The usual mean beta regression model provides the average relationship between a response variable and covariates. However, there are limitations of the conditional mean models, leading, in some cases, to wrong conclusions or, at best, inappropriate statistics. In this article, we extend the usual mean beta regression model using a general and unified parameterization of this distribution that is indexed by some central tendency measure, such as median, mode, arithmetic mean, geometric mean or harmonic mean, and a concentration parameter. In this new regression model, the central tendency measure response is related to a linear predictor through a link function and the linear predictor involves covariates and unknown regression parameters. This approach is naturally robust in the presence of outliers. We also propose a simple interpretation of the predictor response relationship in terms of the percentage increases or decreases in the logarithm of the odds ratio of some central tendency measure of the response. The maximum likelihood method is used for estimating the model parameters. A Monte Carlo experiment is conducted to evaluate the performance of these estimators and residuals in finite samples on the influence of outliers by considering contaminated data under a perturbation scheme to generate outliers were carried out and confirm that the proposed regression model seems to be a new robust alternative for modeling continuous data limited to the unit interval. The usefulness of the new regression model is illustrated through two real applications.