Robust inference under the beta regression model with application to health care studies

Area of Science:

• Statistics
• Biostatistics
• Psychometrics

Background:

• Rates, percentages, and proportions are common in medical biology, health care, and psychology.
• Beta regression models are suitable for response variables bounded between 0 and 1.
• Existing maximum likelihood methods for beta regression lack robustness against outliers.

Purpose of the Study:

• To develop robust inference procedures for the beta regression model.
• To address the lack of robustness in current beta regression methodologies.
• To provide reliable analytical tools for data with outliers.

Main Methods:

• Development of a robust minimum density power divergence estimator.
• Introduction of a class of robust Wald-type tests for beta regression.
• Theoretical analysis of asymptotic properties and robustness using influence functions.

Main Results:

• The proposed methods demonstrate robustness against data contamination and outliers.
• Simulation studies and real-data applications confirm the effectiveness of the new procedures.
• The study provides a more reliable inference framework for beta regression models.

Conclusions:

• Robust statistical inference is crucial for beta regression models, especially in applied fields.
• The developed minimum density power divergence estimator and Wald-type tests offer significant improvements in reliability.
• The findings have practical implications for health care and psychological research.