Jointly modeling rating responses and times with fuzzy numbers: An application to psychometric data

TL;DR

This paper introduces a novel joint modeling approach for ratings and response times using fuzzy numbers, aiming to improve psychometric data analysis by providing a more integrated and statistically sound framework.

Contribution

It proposes a fuzzy number-based probabilistic tree model for jointly analyzing ratings and response times, enhancing interpretability and statistical inference in psychometric studies.

Findings

Fuzzy numbers offer a parsimonious representation of ratings and response times.

The proposed method reduces issues related to multiple hypothesis testing.

Application to real data demonstrates the model's effectiveness.

Abstract

In several research areas, ratings data and response times have been successfully used to unfold the stage-wise 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 regards 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-parameter 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 lead to theoretically sound and more parsimonious data analysis methods, which limit some statistical issues that may occur with standard data analysis procedures (e.g., the problem of multiple hypothesis testing).