The beta regression model is part of a class of models applied to continuous responses restricted to the standard unit interval, such as rates and proportions. Ferrari & Cribari-Neto (2004) proposed the beta regression model incorporating covariates in the mean of the distribution through a link function. However, for studies in which the response variable presents asymmetry and/or discrepant values, this model may not be appropriate. A more convenient measure of central tendency in this situation is the mode of the distribution because of its robustness to outliers and easy interpretation in the presence of asymmetry. Zhou et al. (2020) proposed a parameterization for the beta distribution in terms of the mode and a precision parameter and presented a modal regression model robust to outliers. In this work, we present a more complete study of the modal beta regression properties and performance and a comparison between this model and the usual beta regression model. We perform Monte Carlo simulation studies to evaluate the maximum likelihood estimators under different scenarios of asymmetry and sensitivity to outliers when some patterns of disturbance are imposed. Furthermore, we propose and evaluate three residuals for this class of models. The numerical results suggest that the modal regression model presents a good performance on symmetrical and asymmetrical data and in most scenarios, it performs better in the presence of outliers than the usual beta regression model. Finally, we present and discuss two empirical applications and a comparative analysis of the mean and modal beta regression models.
Fernandes et al. (Thu,) studied this question.