Influence of residuals on Cook’s distance for Beta regression model: Simulation and application

Year 2025, Early Access, 1 - 15

Javaria Ahmad Khan , Atif Akbar , B M Golam Kibria

https://doi.org/10.15672/hujms.1544513

Abstract

Cook’s distance is one of the renowned and classic tools for the detection of influential observations. In this article, we propose to use Cook’s distance with different residuals in the Beta regression model, which is appropriate for modeling the response variable that undertakes a proportion data set. The influence of outlying observations on the basis of its estimated parameters and mean squared error is examined, and performance of residuals is compared. Based on the simulation results and the empirical application, it is observed that the performance of the deviation and weighted residuals is better than that of the rest of the residuals for the detection of influential observations. The observations deleted by the deviance residuals have a large impact on the regression coefficients and on the mean squared error for the Beta regression model.

Keywords

Beta regression, Cook’s distance, outliers, reading skills data, residuals, crude oil conversion data.

References

• [1] M. Amin, M. Amanullah, M. Aslam, and M. Qasim, Influence diagnostics in gamma ridge regression model, J. Stat. Comput. Simul. 89, 536-556, 2019.