Regression diagnostics for binomial data from the forward search

Abstract

We suggest a simple robust method for the detection of atypical and influential observations in binomial data. Our technique is based on a forward search procedure which orders the observations from those most in agreement with a specified generalized linear model to those least in agreement with it. The effectiveness of the forward search estimator in detecting masked multiple outliers, and more generally in ordering binomial data, is shown by means of three data sets. Plots of diagnostic quantities during the forward search clearly show the effect of individual observations on residuals and test statistics. These examples reveal the strength of our method in showing the structure of the data in a way which is more simple and effective than it would be by using standard deletion diagnostic procedures.