New Robust Beta Regression Estimation to Overcome the Effect of High Leverage Points

Abstract

Beta regression models are widely used to model continuous data with a unit interval (0,1), such as ratios, fractions, and rates. The maximum likelihood method is typically used to estimate regression coefficients in beta regression models. However, the maximum likelihood estimator is highly sensitive to outliers. Several studies have proposed methods to address this problem, such as the M-Huber, S-estimator, LMS, and LTS estimators. However, these methods suffer from the problem of high leverage points (HLPoints) in the independent variables. The GM-estimator is one of the methods that address this problem. This study examines beta regression analysis, focusing on the effect of high leverage points (HLPoints) on parameter estimates. Monte Carlo simulations and real data are conducted to evaluate and compare the performance of the proposed robust method, Generalized M-Beta Regression (GMBr), with the existing beta regression method estimated using Maximum Likelihood (MLBr).