On quantile residuals in beta regression

TL;DR

This paper evaluates various residuals in beta regression, demonstrating through simulations that the quantile residual most accurately approximates a standard normal distribution, enhancing model diagnostics.

Contribution

It introduces a comprehensive simulation study comparing residuals in beta regression, highlighting the superior normal approximation of the quantile residual.

Findings

Quantile residuals are better approximated by the normal distribution.

Simulation results favor quantile residuals over others.

Applications confirm the practical usefulness of quantile residuals.

Abstract

Beta regression is often used to model the relationship between a dependent variable that assumes values on the open interval (0,1) and a set of predictor variables. An important challenge in beta regression is to find residuals whose distribution is well approximated by the standard normal distribution. Two previous works compared residuals in beta regression, but the authors did not include the quantile residual. Using Monte Carlo simulation techniques, this paper studies the behavior of certain residuals in beta regression in several scenarios. Overall, the results suggest that the distribution of the quantile residual is better approximated by the standard normal distribution than that of the other residuals in most scenarios. Three applications illustrate the effectiveness of the quantile residual.