Predictive performance of penalized beta regression model for continuous bounded outcomes

Abstract

Prediction models for continuous bounded outcomes are often developed by fitting ordinary least-square regression. However, predicted values from such method may lie outside the range of the outcome as it is bounded within a fixed range, with nonlinear expectation due to the ceiling and floor effects of the bounds. Thus, regular regression models such as normal linear or nonlinear models, are inadequate for prediction purposes for bounded response variable and the use of distributions that can model different shapes are essential. Beta regression, apart from modeling different shapes and constraining predictions to an admissible range, has been shown to be superior to alternative methods for data fitting but not for prediction purposes. We take data structures into account and compared various penalized beta regression method on predictive accuracy for bounded outcome variables using optimism corrected measures. Contrary to results obtained under many regression contexts, the classical maximum likelihood method produced good predictive accuracy in terms of R2 and RMSE. The ridge penalized beta regression performed better in terms of g-index, which is a measure of performance of the methods in external data sets. We restricted attention to prespecified models throughout and as such variable selection methods are not evaluated.