Assessing Influence on Predictions From Generalized Linear Models

Influence diagnostics for predictions from a normal linear model examine the effect of deleting a single case on either the point prediction or the predictive density function. Instead of deleting cases, we apply the local influence method of Cook (1986) to assess the effect of small perturbations of continuous data on a specified point prediction from a generalized linear model. Based on local perturbations of the vector of responses, case weights, explanatory variables, or the components of one case, the diagnostics can detect different kinds of influence. Some of the diagnostics are illustrated with an example and compared to standard diagnostic methods.