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

Antonio Calcagnì,Luigi Lombardi

doi:10.1007/s10182-021-00407-7

Antonio Calcagnì, Luigi Lombardi

Open Access

https://doi.org/10.1007/s10182-021-00407-7

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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.

Highlights

In social and behavioral research, satisfaction surveys, aptitude and personality testing, demographic inquiries, and life quality questionnaires are widespread tools to collect data involving subjective evaluations, agreements, and judgments
In this article we developed a statistical approach to deal with bounded continuous ratings data in the case of non-random uncertainty
Beta fuzzy numbers were adopted to represent ratings data subject to decision uncertainty and the beta regression framework was used to model the random counterpart of the overall rating process

Summary

Introduction

In social and behavioral research, satisfaction surveys, aptitude and personality testing, demographic inquiries, and life quality questionnaires are widespread tools to collect data involving subjective evaluations, agreements, and judgments. It is widely recognized that ratings data often suffer from lack of accuracy, for instance because of social desirability (Furnham 1986), faking behaviors (Lombardi et al 2015), personality (Muthukumarana and Swartz 2014), response styles (Eid and Zickar 2007), and violations of rating rules (Iannario 2015; Preston and Colman 2000; Rabinowitz et al 2019) These issues have been recognized as important by applied statisticians working with ratings data and by several researchers working in fields like applied econometrics (e.g., see Angel et al 2019; De Bruin et al 2011; Zafar 2011), metrology (e.g., see Pendrill and Petersson 2016; Pendrill 2014), and risk analysis (e.g., see Slovic et al 2004)

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