Adjusted quantile residual for generalized linear models

TL;DR

This paper introduces the adjusted quantile residual for generalized linear models, which provides a more accurate and normally distributed diagnostic residual compared to traditional residuals, improving model diagnostics.

Contribution

The paper proposes a new residual for generalized linear models that enhances diagnostic analysis by being closer to normally distributed, outperforming existing residuals.

Findings

Adjusted quantile residual shows better normality properties.

Simulation results favor the new residual over traditional ones.

Application examples demonstrate practical advantages.

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.