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

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 i...

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Vydáno v:Advances in statistical analysis : AStA : a journal of the German Statistical Society Ročník 106; číslo 1; s. 145 - 173
Hlavní autoři: Calcagnì, Antonio, Lombardi, Luigi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022
Springer Nature B.V
Témata:
Algorithms
Applied statistics
Decision making
Econometrics
Economics
Finance
Insurance
Management
Mathematics and Statistics
Modelling
Original Paper
Probability Theory and Stochastic Processes
Ratings
Ratings & rankings
Statistics
Statistics for Business
Uncertainty
Fuzzy ratings data
Decision uncertainty
Customer satisfaction
Fuzzy data analysis
62P25
62-07
Risk-taking behaviors
Beta fuzzy numbers
Beta linear model
62J12
ISSN:1863-8171, 1863-818X
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Shrnutí: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.
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ISSN:1863-8171
1863-818X
DOI:10.1007/s10182-021-00407-7