The Stata module for CUB models for rating data analysis

Many survey questions are addressed as ordered rating variables to assess the extent by which a certain perception or opinion holds among respondents. These responses cannot be treated as objective measures, and a proper statistical analysis to account for their fuzziness is the class of CUB models, acronym of Combination of Uniform and Shifted Binomial (Piccolo and Simone 2019), establishing a different paradigm to model both individual perception (feeling) towards the items and uncertainty. Uncertainty can be considered as a noise for feeling measurement taking the form of heterogeneity of the distribution. CUB models are specified via a two-component discrete mixture to combine feeling and uncertainty modelling. In the baseline version, a shifted Binomial distribution accounts for the underlying feeling and a discrete Uniform accounts for heterogeneity, but different specifications are possible to encompass inflated frequencies, for instance. Featuring parameters can be linked to subjects' characteristics to derive response profiles. Then, different items (possibly measured on scales with different lengths) and groups of respondents can be represented and compared through effective visualization tools. Our contribution is tailored to present CUB modelling to the Stata community by discussing the CUB Module with different case studies to illustrate its applicative extent.