Generalized residuals for outlier detection in ordinal regression models

In ordinal response models residual diagnostics is not commonly used for detecting outliers because generalized models for ordinal data like cumulative models with proportional assumption do not produce standard residuals. In this talk we analyse the generalized residuals introduced by Franses and Paap (2004) which provide signaling tools for observations which are incoherent with the model and therefore potentially anomalous. We also discuss the more recent alternatives: the sign-based statistics (SBS) introduced by Li and Shepherd (2012) and the surrogate residuals introduced by Liu and Zhang (2017) which present nice proprieties even if they are mainly considered for checking the structure of the model, the choice of the link function and possible mixture populations or heteroscedasticity. Hence, we show the utility of the generalized residuals in robust estimation contexts.