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.
The method of paired comparisons (PC) endeavors to rank treatments presented in pairs to panelists (or respondents, judges, jurists, etc.) and they have to select the better one based on sensory evaluations. Sometimes the situations may occur when the panelists cannot discriminate between the treatments and declare a tie. In this study, an effort is made to extend the Weibull PC model to accommodate ties. The extended Weibull PC model is analyzed using Bayesian paradigm. Four different loss functions are used under noninformative (Uniform and Jeffreys) priors. The posterior and marginal posterior distributions are derived. The posterior estimates, posterior risks, preference probabilities, posterior probabilities and predictive probabilities are evaluated to know the ranking of ecological factor. The goodness of the proposed model is assessed. The entire analysis is carried out using a real data set based on the preference for the ecological factors.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.