Robust bootstrap methods in logistic regression model

Bootstrapping is rapidly becoming a popular alternative tool to estimate coefficients and standard errors for logistic regression model. It is now evident that the presence of high leverage points give adverse effect on the classical bootstrap (CB) estimates as its highly dependent on the classical maximum likelihood estimator (MLE). In this paper, we propose two robust bootstrap methods, namely the diagnostic logistic before bootstrap (DLGBB) and the weighted logistic bootstrap with probability (WLGBP) to remedy the effect of high leverage points on bootstrap estimates. The conceptual behind the DLGBB method is to apply resampling with the remaining good observations. Meanwhile, in the WLGBP method probability selection procedure is formulated by assigning lower probability to high leverage points. Medical real data sets are employed to evaluate the performance of the DLGBB and the WLGBP estimates as compared to the CB estimates. The findings signify that the DLGBB is the most efficient method followed by the WLGBP.

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