Quantile-quantile plot for deviance residuals in the generalized linear model

The normal quantile-quantile (Q-Q) plot of residuals is a popular diagnostic tool for ordinary linear regression with normal errors. However, for some generalized linear regression models, the distribution of deviance residuals maybe very far from normality, and therefore the corresponding normal Q-Q plots may be misleading to check model adequacy. We introduce an estimate of the distribution of the deviance residuals of generalized linear models. We propose a new Q-Q plot where the observed deviance residuals are plotted against the quantiles of the estimated distribution. The method is illustrated by the analysis of real and simulated data.