Scalable and robust regression models for continuous proportional data

Area of Science:

• Statistics
• Ecological Modeling

Background:

• Beta regression is standard for proportional data but struggles with outliers and misspecification.
• Existing methods lack robustness and flexibility for complex datasets.

Purpose of the Study:

• Introduce novel cobin and micobin regression models.
• Address limitations of beta regression for continuous proportional data.
• Enhance robustness, computation, and flexibility in statistical modeling.

Main Methods:

• Developed continuous binomial (cobin) and dispersion mixtures of cobin (micobin) distributions.
• Implemented Kolmogorov-Gamma data augmentation for Bayesian computation (Gibbs sampling).
• Applied models to analyze benthic macroinvertebrate data using lake watershed covariates.

Main Results:

• Cobin and micobin models demonstrate superior robustness compared to beta regression.
• Models effectively handle responses at boundary values (0 or 1).
• Simulation experiments and real-data analysis confirm computational efficiency and flexibility.

Conclusions:

• Cobin and micobin regression offer significant improvements over traditional beta regression.
• The Kolmogorov-Gamma scheme enables efficient Bayesian analysis for complex data structures.
• These models provide a powerful tool for analyzing ecological and other proportional data.