Robust estimation in beta regression via maximum Lq-likelihood

TL;DR

This paper introduces a robust estimation method for beta regression models using maximum Lq-likelihood, improving resistance to outliers while maintaining efficiency, with practical applications and diagnostic tools.

Contribution

It develops a new robust estimation procedure for beta regression based on reparameterized Lq-likelihood, including a data-driven method for tuning parameter selection.

Findings

Robust estimators show high resistance to outliers in simulations.

The method maintains efficiency when no outliers are present.

Residual diagnostics effectively identify outliers.

Abstract

Beta regression models are widely used for modeling continuous data limited to the unit interval, such as proportions, fractions, and rates. The inference for the parameters of beta regression models is commonly based on maximum likelihood estimation. However, it is known to be sensitive to discrepant observations. In some cases, one atypical data point can lead to severe bias and erroneous conclusions about the features of interest. In this work, we develop a robust estimation procedure for beta regression models based on the maximization of a reparameterized Lq-likelihood. The new estimator offers a trade-off between robustness and efficiency through a tuning constant. To select the optimal value of the tuning constant, we propose a data-driven method which ensures full efficiency in the absence of outliers. We also improve on an alternative robust estimator by applying our data-driven method to select its optimum tuning constant. Monte Carlo simulations suggest marked robustness of the two robust estimators with little loss of efficiency. Applications to three datasets are presented and discussed. As a by-product of the proposed methodology, residual diagnostic plots based on robust fits highlight outliers that would be masked under maximum likelihood estimation.