Title: Residuals diagnostics for the choice of model-based trees for ordinal responses
Authors: Rosaria Simone - University of Naples Federico II (Italy) [presenting]
Abstract: Model-based profiling of preferences and evaluations, when collected as either rating or marginal ranking data, can be successfully pursued by means of classification and regression trees. In this regard, the model-based approach should adopt flexible and parsimonious models for the tree nodes in order to enable the understanding of the rating process and the derivation of response profiles. CUBREMOT is a class of model-based binary trees for preference and evaluation data that is grounded on the specification of CUB models, of which the Binomial is a particular case. The flexibility of CUBREMOT in shaping rating data at different subsetting levels, also in presence of some structural inflated categories, is enhanced by diagnostic checks in terms of residuals. For ordinal responses, the analysis of residuals built via a jittering approach to perform model selection can be useful to assess the goodness of the derived classification, to choose the best baseline model, to identify the best splitting criterion (if more are available), or to tune the tree depth for the post-pruning phase. The proposal is discussed on the basis of several data examples to show its efficacy and the extent of its applicability.