Deletion Diagnostics in Logistic Regression

Abstract

Today, there are not many good measures for detecting influential observations in case of fitting a logistic regression model. So, the purpose of this article is to extrapolate from the pre-existing deletion diagnostics defined for detecting influential points for multiple linear regression, i.e. the DFFITS, DFBETAS and Cook's Distance to the scenario of a binary logistic regression model and then view the multinomial model as a special case of the same. The threshold for determining whether an observation is an influential observation or not is judged using the asymptotic distribution of the Cook's Distance in the multinomial setting, both for the single and the group deleted case. The results are examined under various simulation scenarios as well as over the modified Kyphosis data-set.