Residuals and diagnostics for binary and ordinal regression models: An introduction to the sure package

Abstract

Residual diagnostics is an important topic in the classroom, but it is less often used in practice when the response is binary or ordinal. Part of the reason for this is that generalized models for discrete data, like cumulative link models and logistic regression, do not produce standard residuals that are easily interpreted as those in ordinary linear regression. In this paper, we introduce the R package sure, which implements a recently developed idea of SUrrogate REsiduals. We demonstrate the utility of the package in detection of cumulative link model misspecification with respect to mean structures, link functions, heteroscedasticity, proportionality, and interaction effects.