Robust methods in binary logistics regression

The regression analysis method applied when the dependent variable is discrete is called logistic regression analysis. One of the purposes of logistic regression analysis is classification, and the other is to establish a generally acceptable model that can describe the relationship between dependent and independent variables in a way that has the best fit by using the fewest variables. As in linear regression analysis, multicollinearity and outlier problems can be encountered in logistic regression analysis. In case of multicollinearity between independent variables, the obtained regression coefficients will not reflect their true values. In case of outliers in the data set, these values should be determined and their effects on parameter estimations should be examined. For the solutions of these problems, different estimators have been proposed in the literature. In this thesis study, a robust biased estimator is proposed to solve these two problems together in case of both multicollinearity and outlier problems in the data set. This proposed estimator was compared with other estimators available in the literature according to the mean square error (MSE) criterion. Simulation study was supported with real data application. In addition, robust diagnostic methods and robust cut-off values for these methods were proposed with the help of the methods available in the literature for the outliers in the data set.