The Maxwell paired comparison model under Bayesian paradigm using informative priors

• Published in: Communications in statistics. Theory and methods Vol. 51; no. 2; pp. 301 - 312
• Main Authors: Kifayat, Tanveer, Aslam, Muhammad, Cheema, Salman Arif
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 17-01-2022; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Dirichlet problem; Drinking water; Elicitation of hyperparameters; informative priors; paired comparison; Parameter estimation
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2020.1748198

In paired comparison (PC) experiments, items are judged on subjective criterion in order to decide which of the two objects is preferable. A new PC model is developed and analyzed under Bayesian framework using two informative priors - conjugate prior and Dirichlet prior. The hyperparameters are elicited through the prior predictive distribution approach. The proposed model is employed to analyze the preference data of brands of drinking water. We consider two data sets with the sample sizes of 5 and 35 to explore the small and large sample behaviors of the proposed model. It is observed that the proposed model is capable of retaining the underlying preference ordering in both small and large sample scenarios. The conclusions are based on elicited values of worth parameters, estimated preference probabilities, and Bayes factor.