When regressors exhibit a linear correlation in the Beta regression model (BRM), the Beta ridge regression model (BRRM) is employed to mitigate the impact of multicollinearity on maximum likelihood estimation (MLE) in the BRM. The traditional MLE approach is particularly sensitive to such correlations, leading to unstable and unreliable parameter estimates. To identify the influential data points, Cook’s distance is utilized as a classic diagnostic tool to detect outliers. This paper emphasizes the dual challenges posed by multicollinearity and outliers, proposing a set of estimators for the shrinkage parameter in BRM using Cook’s distance in combination with varied residual types. For illustrative purposes, Monte Carlo simulations and real data are presented.
The empirical results indicate that certain classes of weighted residuals (W, SW, ASW, and SW2) demonstrate superior performance in detecting outliers, with a high percentage of detection across different scenarios. Additionally, findings suggest that the outlier detection is not only influenced by the residual weighting scheme but is also inclined by the severity of multicollinearity and the selected value of the shrinkage parameter k. These results provide a baseline for further refinement of BRM, potentially in the selection of optimal shrinkage parameter and residual type, involving multicollinearity and contaminated data.