Self-Selecting Robust Logistic Regression Model

Abstract

Logistic regression model is the most common model used for the analysis of binary data. However, the problem of atypical observations in the data has an unduly effect on the parameter estimates. Many researchers have developed robust statistical model to solve this problem of outliers. Gelman (2004) proposed GRLR, a robust model by trimming the probability of success in LR. The trimming values in this model were fixed and the user is required to specify this value well in advance. In particular this study developed SsRLR model by allowing the data itself to select the alpha value. We proposed a Restricted LR model to substitute the LR in presence of outliers. We proved that the SsRLR model is the more robust to the presence of leverage points in the data. Parameter estimations is done using a full Bayesian approach implemented in WinBUGS 14 software.