Robust Diagnostic Deletion Techniques in Linear and Logistic Regression

Abstract

Identification of unexpected observations is a topic of great attention in modem regression analysis. At the beginning statisticians differ but now they recognize robust regression and regression diagnostics are two complementary remedies to study unusual observations. We use both of them for identifying irregular observations at a time. We find out the group deletion diagnostic methods that show better performance for identifying influential observations in linear regression. These are based on robust regression and/or relevant diagnostic methods so that these are free from huge computational tasks and reliable in presence of masking and/or swamping because of prior suspect-group identification. We find a technique that performs well in case of large number and high-dimensional data sets. We have done a classification task of unusual observations in linear regression according to their nature of consequences on the analysis, and model building process. At the same time the method performs well for identifying influential observations. This method may be a good addition to the existing graphical literature. We have seen that our proposed procedures in linear regression are also effective to the logistic regression after some modification and development to the existing identification techniques in linear regression. Our further contribution is to propose two new identification techniques for influential observations in logistic regression. The new methods show efficient performance for the proper identification of unusual observations and thereby provide less misclassification error in the response variable for the binomial logistic regression. Summarizing all the above issues we can say that we have made contribution in three areas: identification of influential observations in linear regression, classification of unusual observations in linear regression, and identification of unusual observations in logistic regression.