Selecting and checking a binomial response generalized linear model using phi-divergences

This work introduces specific tools based on phi-divergences to select and check generalized linear models with binary data. A backward selection criterion that helps to reduce the number of explanatory variables is considered. Diagnostic methods based on divergence measures such as a new measure to detect leverage points and two indicators to detect influential points are introduced. As an illustration, the diagnostics are applied to human psychology data.