Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data
Abstract
:1. Introduction
2. Methodology
2.1. Fuzzy Numbers
2.2. From IRTree to fIRTree
- Define and fit an IRTtree model to in order to obtain and
- Plug-in and into Equation (5) to obtain the estimated probability distribution
- Compute mode and precision of the fuzzy number via the following equalities:
- Compute left and right bounds using link equations:
- Compute the fuzzy membership function:
- Compute the intensification parameter:
2.3. Fuzzy Normal Linear Model with Crisp Predictors
3. Application
3.1. Data and Variables
3.2. Data Analysis and Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Models | () | (1 − %) CI |
---|---|---|
Normal Linear Model | ||
Residuals quantiles: Q1: −0.555, Med: −0.041, Q3: 0.611 | ||
(Intercept) | 4.204 (0.211) | [3.788, 4.621] |
religiousness (No vs. Yes) | −0.146 (0.135) | [−0.412, 0.120] |
emotional_stability | −0.232 (0.029) | [−0.289, 0.174] |
university (No vs. Yes) | −0.280 (0.119) | [−0.516, −0.044] |
pseudo- | ||
Log-Normal Model | ||
Residuals quantiles: Q1: −0.298, Med: −0.060, Q3: 2.427 | ||
(Intercept) | 0.138 (58.573) | [7.792, 8.336] |
religiousness (No vs. Yes) | 0.256 (0.088) | [0.083, 0.429] |
emotional_stability | 0.003 (0.019) | [−0.034, 0.041] |
university (No vs. Yes) | 0.162 (0.078) | [0.008, 0.316] |
pseudo- | ||
Fuzzy Normal Linear Model | ||
Residuals quantiles: Q1: −0.287, Med: 0.068, Q3: 0.737 | ||
(Intercept) | 3.383 (0.259) | [2.870,3.894] |
religiousness (No vs. Yes) | −0.169 (0.152) | [−0.469,0.130] |
emotional_stability | −0.127 (0.034) | [−0.195, −0.060] |
university (No vs. Yes) | −0.172 (0.134) | [−0.436, 0.093] |
pseudo- |
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Cao, N.; Calcagnì, A. Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data. Mathematics 2022, 10, 1025. https://doi.org/10.3390/math10071025
Cao N, Calcagnì A. Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data. Mathematics. 2022; 10(7):1025. https://doi.org/10.3390/math10071025
Chicago/Turabian StyleCao, Niccolò, and Antonio Calcagnì. 2022. "Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data" Mathematics 10, no. 7: 1025. https://doi.org/10.3390/math10071025
APA StyleCao, N., & Calcagnì, A. (2022). Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data. Mathematics, 10(7), 1025. https://doi.org/10.3390/math10071025