Robustness issues for CUB models

The present paper deals with a parametric class of models implemented forordered categorical data, denoted as cub model, which is defined as a discretemixtureof a shifted binomial and a uniform random variable. For these models, robustnessissues are considered. In particular, the influence function is introduced and subsequentlyused to define the robustness measures for categorical data. By exploiting thepeculiar parametrization of the cub models, diagnostic plots are proposed which allowto 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 todetermine an upper bound. The paper provides evidence that, despite the limited rangeof the support, contaminations in the data can heavily affect the inferential proceduresand hence robustness topics are indeed relevant for ordinal data.