Residual Diagnostics for Interpreting CUB Models

CUB models represent a new approach for the analysis of categorical ordinal data fitted by maximum likelihood methods. The relevant domain of study is the specification and estimation of the behaviour of respondents when faced to ratings data by analysing the relationship among ordinal scores and observed covariates. The use of such models has become very common in recent year; thus, there is need 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 an extension and implementation of a specific graphical methodology, known as binned residual diagnostic, in order to check the adequacy of fitted CUB models and/or infer about improvements of the maintained model. Such proposals will be illustrated through the analysis of real data.