View article

Examining residuals is a crucial step in statistical analysis to identify the discrepancies between models and data, and assess the overall model goodness-of-fit. In diagnosing normal linear regression models, both Pearson and deviance residuals are often used, which are equivalently and approximately standard normally distributed when the model fits the data adequately. However, when the response vari*able is discrete, these residuals are distributed far from normality and have nearly parallel curves according to the distinct discrete response values, imposing great challenges for visual inspection.

Randomized quantile residuals (RQRs) were proposed in the literature by Dunn and Smyth (1996) to circumvent the problems in traditional residuals. However, this approach has not gained popularity partly due to the lack of …