Cressie and Read power-divergences as influence measures for logistic regression models

Abstract

A sample version of the power-divergence measures of Cressie and Read is proposed for the influence analysis in the logistic regression model. Influence measures are obtained by quantifying the deviation between the sample distribution of an estimate obtained with all the observations and the sample distribution of the same estimate obtained without any observation. In particular, this approach is applied to three estimates of the model: the MLE of regression coefficients vector, the probabilities vector and the linear predictor of a future case. Some examples are considered to clarify the usefulness of the introduced diagnostics.