Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data

Niccolò Cao and Antonio Calcagnì
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Niccolò Cao: DPSS, University of Padova, 35131 Padova, Italy
Antonio Calcagnì: DPSS, University of Padova, 35131 Padova, Italy

Mathematics, 2022, vol. 10, issue 7, 1-11

Abstract: In several research areas, ratings data and response times have been successfully used to unfold the stagewise process through which human raters provide their responses to questionnaires and social surveys. A limitation of the standard approach to analyze this type of data is that it requires the use of independent statistical models. Although this provides an effective way to simplify the data analysis, it could potentially involve difficulties with regard to statistical inference and interpretation. In this sense, a joint analysis could be more effective. In this research article, we describe a way to jointly analyze ratings and response times by means of fuzzy numbers. A probabilistic tree model framework has been adopted to fuzzify ratings data and four-parameters triangular fuzzy numbers have been used in order to integrate crisp responses and times. Finally, a real case study on psychometric data is discussed in order to illustrate the proposed methodology. Overall, we provide initial findings to the problem of using fuzzy numbers as abstract models for representing ratings data with additional information (i.e., response times). The results indicate that using fuzzy numbers leads to theoretically sound and more parsimonious data analysis methods, which limit some statistical issues that may occur with standard data analysis procedures.

Keywords: fuzzy rating data; fuzzy statistics; fuzzy linear regression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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