Adjusted quantile residual for generalized linear models

Abstract: Generalized linear models are widely used in many areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in generalized linear models using residuals that are approximately standard normally distributed. Diagnostic analysis in this class of models are usually performed using the standardized Pearson residual or the standardized deviance residual. The former has skewed distribution and the latter has negative mean, specially when the variance of the response variable is high. In this work, we introduce the adjusted quantile residual for generalized linear models. Using Monte Carlo simulation techniques and two applications, we compare this residual with the standardized Pearson residual, the standardized deviance residual and two other residuals. Overall, the results suggest that the adjusted quantile residual is a better tool for diagnostic analysis in generalized linear models.