Bayesian Analysis of Paired Comparison Model using Jeffreys Prior
[1]
Amna Nazeer, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China.
[2]
Sadia Qamar, Department of Statistics, University of Sargodha, Sargodha, Pakistan.
[3]
Samina Satti, Department of Statistics, University of Wah, WahCantt, Pakistan.
Paired comparison is very old and reliable psychometric scheme. Baaren in 1978 presented new extensions of the paired comparison models. This study contains the Bayesian analysis of the Baaren model-IV using non-informative Jeffreys prior. The paired comparison model includes the treatment/worth, tie and within pair order effect parameters. Four treatments are used for the numerical evaluation of the model. Due to the complex description of the Jeffreys prior for the current study, it has been approximated numerically. Gibbs sampling method has been used for the approximation of the findings. The joint posterior distribution was then obtained and used to compute the posterior means, posterior modes and posterior standard deviations. The findings supported the existence of the order effect i.e. the treatment presented first had an edge of being preferred in the pair wise comparison. The preference and posterior probabilities of the model also supported the findings of the posterior estimates. The X2 test declared the model appropriate for the under study data set with high probability.
Paired Comparison Model, Bayesian Inference, Jeffreys Prior, Posterior Estimates, Preference Probabilities
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