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Mixture models for ordinal responses in the tradition of cub models use the uniform distribution to account for uncertainty of respondents. A model is proposed that uses more flexible distributions in the uncertainty component: the discretized Beta distribution allows to account for response styles, in particular the preference for middle or extreme categories. The proposal is compared with traditional cub models in simulation studies and its use is illustrated by two applications.

Ordinal responses in the form of ratings arise frequently in social sciences, marketing and business applications where preferences, opinions and perceptions play a major role and it is common to collect along with rater’s evaluation, a set of covariates that characterize the respondent and/or the item/service. In this framework, the ordinal nature of the response has to be properly taken into account when the interest is in the understanding of different response patterns in terms of subjects’ covariates. In this spirit, a model-based tree procedure for ordinal scores is illustrated: its structure is based on a class of mixture models for ordinal rating data that implies a twofold analysis in terms of feeling and uncertainty and effective graphi- cal visualization of results. The chosen modelling framework entails that the splitting criterion can be customized according to the purposes of the study and the available data. Thus, the selection of variables yielding to the best partitioning results is driven by fitting measures or classical likelihood and deviance measurements, for instance. In order to illustrate the performances of the different splitting criterion for the cubremot procedure, we consider data from the 5th European Working Condition Survey carried out by Eu- rofound in 2010, comparison with alternative approaches that grow trees for ordinal responses is also outlined.