A renovated cook’s distance based on the Buckley-James estimate in censored regression - Aziz, Nazrina; Dong, Qian Wang (2009)
There have been various methods created based on the regression ideas to resolve the problem of data set containing censored observations, i.e. the Buckley-James method, Miller’s method, Cox method, and Koul-Susarla-Van Ryzin estimators.Even though comparison studies show the Buckley-James method performs better than some other methods, it is still rarely used by researchers mainly because of the limited diagnostics analysis developed for the Buckley-James method thus far.Therefore, a diagnostic tool for the Buckley-James method is proposed in this paper.It is called the renovated Cook’s Distance, (RD∗ i ) and has been developed based on the Cook’s idea.The renovated Cook’s Distance (RD∗i ) has advantages (depending on the analyst demand) over (i) the change in the fitted value for a single case, DFIT∗i as it measures the influence of case i on all n fitted values ˆY ∗i (not just the fitted value for case i as DFIT∗ i) (ii) the change in the estimate of the coefficient when the ith case is deleted, DBETA∗ i since DBETA∗ i corresponds to the number of variables p so it is usually easier to look at a diagnostic measure such as RD∗i since information from p variables can be considered simultaneously. Finally, an example using Stanford Heart Transplant data is provided to illustrate the proposed diagnostic tool.