CUBREMOT: A tool for building model-based trees for ordinal responses

The paper introduces a new technique for growing trees for ordinal responses in the model-based framework. We consider the class of CUB mixtures which is particularly appropriate to model perceptions and evaluations, as it designs the response process as the combination of a personal feeling and an inherent uncertainty. In our proposal, the partitioning process is based on the local estimation of CUBregression models to profile responses according to feeling and uncertainty conditional to the splitting variables. In this regard, two alternative splitting criteria are introduced featuring both inferential and fitting issues. Moreover, the chosen modelling framework allows for advantageous visualization of the classification results. The proposal is illustrated using real data from a survey conducted by the Italian National Statistical Office, with focus on perceived trust towards the European Parliament. A benchmark study is conducted to settle the proposal among the available tree methods for ordinal responses.