Comparative Evaluation of Classical Robust and Wavelet Enhanced Beta Regression Models for Proportional Data

Abstract

This paper presents a comprehensive comparative modeling of conventional, robust, and wavelet-augmented beta regression models in continuous lineage modeling. To preprocess the response variable, four discrete wavelet transforms—Daubechies IV, Coiflet IV, Simlet IV, and discrete Meyer (Dmey) were applied to remove noise and enhance model robustness. Performance was evaluated by conducting extensive Monte Carlo simulations using different sample sizes and numbers of predictors, where outliers were artificially incorporated to represent the overlap of the real data. The root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R^2) were used as measures of model performance. Results demonstrated that wavelet-enhanced models surpassed conventional and resilient Beta regression at all points, where filter Coiflets 4 and Symlets 4 produced the highest predictive precision and resilience. The wavelet pre-processing effectively eliminated noise and outlier influences, producing more precise and smoother forecasts. The developed models were also applied to a real body composition data set and were shown to replicate the simulation results as well as demonstrate real-world utility. This combined strategy focuses on the necessity of combining wavelet signal processing with stable regression procedures for better analysis of bounded continuous data with outliers.