Residual diagnostics for interpreting CUB models

Abstract

CUB models represent a new approach for the analysis of categorical ordinal data. The relevant domain of study is the specification and estimation of the behaviour of respondents when faced to ratings by analysing the relationship among ordinal scores and observed covariates. The increasing use of such models suggests to delve into the issue of appropriate residuals to be used for diagnostic purposes. In fact, the discreteness of the response variable discourages the use of standard regression paradigms. In this context, we propose the extension and implementation of a specific graphical methodology, known as binned residual plots, in order to check the adequacy of fitted CUB models and/or infer about improvements of the maintained model. Such proposals have been exemplified through the analysis of real data.