Robust estimation in beta regression via maximum L$$_q$$-likelihood

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