Deviance residuals in generalised log-gamma regression models with censored observations

Abstract

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Keywords:

• Censoring data
• Deviance
• Generalised gamma distribution
• Residual analysis
• Survival data analysis

Acknowledgements

This work was partly supported by CNPq and FAPESP, Brazil. The authors thank the Associate Editor and one anonymous referee for valuable suggestions.