Robustness issues for cub models

The present paper deals with a parametric class of models implemented for ordered categorical data, denoted as cub model, which is defined as a discrete mixture of a shifted binomial and a uniform random variable. For these models, robustness issues are considered. In particular, the influence function is introduced and subsequently used to define the robustness measures for categorical data. By exploiting the peculiar parametrization of the cub models, diagnostic plots are proposed which allow to display the effect of a contamination in the data, simultaneously for all categories. The breakdown point is also considered and a computational procedure is suggested to determine an upper bound. The paper provides evidence that, despite the limited range of the support, contaminations in the data can heavily affect the inferential procedures and hence robustness topics are indeed relevant for ordinal data.