A probabilistic tree model to analyze fuzzy rating data

TL;DR

This paper introduces a probabilistic tree model for analyzing fuzzy rating data in psychometric assessments, combining multinomial and binomial distributions with decision trees to capture the stage-wise mechanisms of fuzzy responses.

Contribution

It proposes a novel probabilistic tree model that effectively represents fuzzy rating responses and estimates parameters using marginal maximum likelihood.

Findings

Model successfully captures fuzzy rating mechanisms

Application to real data demonstrates model's practical utility

Provides initial insights into modeling fuzzy responses in psychometrics

Abstract

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.