  In this contribution we provide initial findings to the problem of modeling
fuzzy rating responses in a psychometric modeling context. In particular, we
study a probabilistic tree model with the aim of representing the stage-wise
mechanisms of direct fuzzy rating scales. A Multinomial model coupled with a
mixture of Binomial distributions is adopted to model the parameters of LR-type
fuzzy responses whereas a binary decision tree is used for the stage-wise
rating mechanism. Parameter estimation is performed via marginal maximum
likelihood approach whereas the characteristics of the proposed model are
evaluated by means of an application to a real dataset.
