The beta regression model (BRM) is a popular and widely applied modeling approach, especially when dealing with data bounded within the interval (0, 1). It has been used extensively in various fields, including chemistry, environmental science, medicine, and biology. BRM aims to estimate unknown model parameters, typically achieved using the maximum likelihood estimator (MLE). However, MLE is not without limitations. It can be highly sensitive to multicollinearity and outliers, which can distort coefficient estimates, lead to misleading conclusions, and inflate variance, ultimately increasing the mean squared error (MSE). To address these challenges, this study proposed new robust estimators for BRM that incorporated robust modified ridge-type estimators. These estimators were specifically designed to reduce the adverse effects of multicollinearity and outliers. Their performance was theoretically compared to that of the traditional MLE and robust ridge estimators. In addition, an extensive simulation study was carried out in various scenarios to evaluate their effectiveness. Both theoretical comparisons and simulation results demonstrated the clear advantages of the proposed robust estimators in managing multicollinearity and handling outliers. To further validate the findings, the estimators were applied to real-world data from breast cancer patients. The results confirmed that the proposed robust estimators offer greater robustness and reliability compared to MLE and robust ridge methods. These findings highlighted the practical importance of using robust estimation techniques to improve the accuracy and dependability of BRMs, particularly in empirical research involving highly multicollinear and outlier data.
Citation: Ali T. Hammad, I. Elbatal, Ehab M. Almetwally, M. M. Abd El-Raouf, M. A. El-Qurashi, Ahmed M. Gemeay. A novel robust estimator for addressing multicollinearity and outliers in Beta regression: simulation and application[J]. AIMS Mathematics, 2025, 10(9): 21549-21580. doi: 10.3934/math.2025958
The beta regression model (BRM) is a popular and widely applied modeling approach, especially when dealing with data bounded within the interval (0, 1). It has been used extensively in various fields, including chemistry, environmental science, medicine, and biology. BRM aims to estimate unknown model parameters, typically achieved using the maximum likelihood estimator (MLE). However, MLE is not without limitations. It can be highly sensitive to multicollinearity and outliers, which can distort coefficient estimates, lead to misleading conclusions, and inflate variance, ultimately increasing the mean squared error (MSE). To address these challenges, this study proposed new robust estimators for BRM that incorporated robust modified ridge-type estimators. These estimators were specifically designed to reduce the adverse effects of multicollinearity and outliers. Their performance was theoretically compared to that of the traditional MLE and robust ridge estimators. In addition, an extensive simulation study was carried out in various scenarios to evaluate their effectiveness. Both theoretical comparisons and simulation results demonstrated the clear advantages of the proposed robust estimators in managing multicollinearity and handling outliers. To further validate the findings, the estimators were applied to real-world data from breast cancer patients. The results confirmed that the proposed robust estimators offer greater robustness and reliability compared to MLE and robust ridge methods. These findings highlighted the practical importance of using robust estimation techniques to improve the accuracy and dependability of BRMs, particularly in empirical research involving highly multicollinear and outlier data.
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Ali T. Hammad, I. Elbatal, Ehab M. Almetwally, M. M. Abd El-Raouf, M. A. El-Qurashi, Ahmed M. Gemeay. A novel robust estimator for addressing multicollinearity and outliers in Beta regression: simulation and application[J]. AIMS Mathematics, 2025, 10(9): 21549-21580. doi: 10.3934/math.2025958
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