Modeling random and non-random decision uncertainty in ratings data: A fuzzy beta model

TL;DR

This paper introduces a fuzzy beta model that captures both random and non-random decision uncertainties in ratings data, providing a nuanced statistical approach for analyzing imprecise human responses.

Contribution

It presents a novel fuzzy beta model incorporating decision uncertainty into ratings analysis, utilizing a fuzzy EM algorithm for parameter estimation.

Findings

Model effectively captures decision uncertainty in ratings.

Simulation and case studies validate the model's applicability.

Provides a new tool for analyzing imprecise human ratings.

Abstract

Modeling human ratings data subject to raters' decision uncertainty is an attractive problem in applied statistics. In view of the complex interplay between emotion and decision making in rating processes, final raters' choices seldom reflect the true underlying raters' responses. Rather, they are imprecisely observed in the sense that they are subject to a non-random component of uncertainty, namely the decision uncertainty. The purpose of this article is to illustrate a statistical approach to analyse ratings data which integrates both random and non-random components of the rating process. In particular, beta fuzzy numbers are used to model raters' non-random decision uncertainty and a variable dispersion beta linear model is instead adopted to model the random counterpart of rating responses. The main idea is to quantify characteristics of latent and non-fuzzy rating responses by means of random observations subject to fuzziness. To do so, a fuzzy version of the Expectation-Maximization algorithm is adopted to both estimate model's parameters and compute their standard errors. Finally, the characteristics of the proposed fuzzy beta model are investigated by means of a simulation study as well as two case studies from behavioral and social contexts.