Journal of Statistics Applications & Probability

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The multiple logistic regression model is commonly used in scientific researches. It is a regression model with more than two categories of response variable and multi explanatory variables. The conventional maximum likelihood estimator (MLE) is widely used to determine parameter values. It is used because it is famous and easy to apply. However, this estimator is highly sensitive to leverage points and outliers. The main objective of this research is to get the best estimation of the multiple logistic regression parameters with problem of leverage points. Two robust estimators based on robust Mahalanobis distance (RMD) are established. They are named (MLERMD1 and MLERMD2). The proposed robust methods are compared with MLE and some other famous robust methods. The bias and mean square error are considered as measures for comparison. Simulation study is conducted with different sample sizes and percentages of leverage points. Besides, real example data are applied to compare among the methods. Results of simulation and real example show that the performance of the proposed methods (MLERMD1 and MLERMD2) is more efficient than those of MLE and the other robust methods. The MLERMD2 have the least values of bias and mean square error with different percentage of leverage points.

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