Abstract
The method of paired comparisons (PC) is widely used to rank items using sensory evaluations. The PC models are developed to provide basis for such comparisons. In this study, the Weibull PC model is analyzed under the Bayesian paradigm using noninformative priors and different loss functions, namely, Squared Error Loss Function (SELF), Quadratic Loss Function (QLF), DeGroot Loss Function (DLF), and Precautionary Loss Function (PLF). Numerical approximation is used to illustrate the entire estimation procedure. A real dataset showing usage preferences for different cellphone brands, Huawei (HW), Samsung (SS), Oppo (OP), QMobile (QM), and Nokia (NK), is used. Quadrature method is used to evaluate the Bayes estimates, their posterior risks, preference probabilities, predictive probabilities, and posterior probabilities to establish and verify ranking order of the competing cellphone brands under study. The results show that the paired comparison model under the study using Bayesian approach involving various loss functions can offer mathematical approach to evaluate cellphone brand preferences. The ranking provided by the model is justifiable according to the usage preference for these cellphone brands. The ranking given by the model indicates that cellphone brand Samsung is preferred the most and QMobile is the least preferred. The plausibility of the model is also assessed using the Chi square test of goodness of fit.
Highlights
Paired Comparison (PC) is a very helpful technique for comparing and prioritizing the objects under subjective judgments, when quantitative measurements are either not available or accurate assessments are not possible. is technique is known as special rank order technique
Results show that Posterior Risk (PR) for the parameters of cj, j 1, 2, ..., 5 under Squared Error Loss Function (SELF) are smaller when compared to the remaining loss functions: DeGroot Loss Function (DLF), Precautionary Loss Function (PLF), and Quadratic Loss Function (QLF). us, the results clearly show that SELF is the most suitable loss function for the estimation of model’s parameters c1, c2, c3, c4, and c5
Conclusion e Weibull PC model is analyzed under Bayesian paradigm using noninformative (Uniform and Jeffreys) priors through numerical approximation. e dataset for the usage preferences of the cellphone brands is collected from the people living in Islamabad, Pakistan, and used for the Bayesian analysis. e posterior distributions are derived and the posterior estimates are obtained under various loss functions such as Squared Error Loss Function, Quadratic Loss Function, DeGroot Loss Function, and Precautionary Loss Function. e graphical representation of the marginal posterior distributions of the model parameters has revealed the symmetry of the distributions of the parameters
Summary
Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation. E method of paired comparisons (PC) is widely used to rank items using sensory evaluations. Quadrature method is used to evaluate the Bayes estimates, their posterior risks, preference probabilities, predictive probabilities, and posterior probabilities to establish and verify ranking order of the competing cellphone brands under study. E results show that the paired comparison model under the study using Bayesian approach involving various loss functions can offer mathematical approach to evaluate cellphone brand preferences. E ranking provided by the model is justifiable according to the usage preference for these cellphone brands. E ranking given by the model indicates that cellphone brand Samsung is preferred the most and QMobile is the least preferred. Quadrature method is used to evaluate the Bayes estimates, their posterior risks, preference probabilities, predictive probabilities, and posterior probabilities to establish and verify ranking order of the competing cellphone brands under study. e results show that the paired comparison model under the study using Bayesian approach involving various loss functions can offer mathematical approach to evaluate cellphone brand preferences. e ranking provided by the model is justifiable according to the usage preference for these cellphone brands. e ranking given by the model indicates that cellphone brand Samsung is preferred the most and QMobile is the least preferred. e plausibility of the model is assessed using the Chi square test of goodness of fit
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