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Bayesian Analysis of Paired Comparison Model using Jeffreys Prior
Current Issue
Volume 3, 2015
Issue 6 (December)
Pages: 38-41   |   Vol. 3, No. 6, December 2015   |   Follow on         
Paper in PDF Downloads: 106   Since Jan. 5, 2016 Views: 1622   Since Jan. 5, 2016
Authors
[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.
Abstract
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.
Keywords
Paired Comparison Model, Bayesian Inference, Jeffreys Prior, Posterior Estimates, Preference Probabilities
Reference
[1]
David, H. A., (1988). The Method of Paired Comparisons. 2nd Eds. London: Griffin.
[2]
Bradley, R. A. (1976). A biometrics invited paper. science, statistics, and paired comparisons. Biometrics, 32, 213-239.
[3]
Bradley, R. A., & Terry, M. E. (1952). Rank analysis of Incomplete Block Designs, I. The method of Paired Comparisons. Biometrika, 39, 324-345.
[4]
Rao, P. V., & Kupper, L. L. (1967). Ties in Paired-Comparison Experiments: A Generalization of Bradley-Terry Model. Journal of the American Statistical Association, 62, 194-204.
[5]
Davidson, R. R. (1970). On Extending the Bradley-Terry Model to Accommodate Ties in the Paired comparison Experiments. Journal of the American Statistical Association, 65, 317-328.
[6]
Davidson, R. R., & Beaver, R. J. (1977). On Extending the Bradley-Terry Model to Incorporate Within Pair Order Effects. Biometrics, 33, 693-702.
[7]
Baaren, A. V. (1978). On a Class of Extension to the Bradley-terry Model in Paired Comparisons. Statistica Neerlandica, 32, 57-67.
[8]
Trawinski, B. J. (1965). An Exact Probability Distribution over Sample Spaces of Paired Comparisons. Biometrics, 21, 986-1000.
[9]
Singh, J. (1976). A Note on Pair Comparison Rankings. The Annals of Statistics, 4(3), 651-654.
[10]
Lancaster, J. F., & Quade, D. (1983). Random Effect in the Paired Comparison Experiments Using the Bradley-Terrey Model. Biometrics, 39, 245-249.
[11]
Dittrich, R., Hatzinger, R., & Katzenbeisser, W. (1998). Modeling the Effect of Subject-Specific Covariates in Paired Comparison Studies with an Application to University Ranking. Journal of the Royal Statistical Society: Series C (Applied Statistics), 47, 511-525.
[12]
Glickman, M. E., (1999). Parameters Estimation in Large Dynamic Paired Comparison Experiment. Applied Statistics, 48, 377-394.
[13]
Abbas, N., & Aslam, M. (2009). Prioritizing the Items through Paired Comparison Models. A Bayesian Approach. Pakistan Journal of Statistics, 25, 59-69.
[14]
Davidson, R. R., & Solomon, D. L. (1973). A Bayesian Approach to Paired Comparison Experiments. Biometrika, 60(3), 477-487.
[15]
Leonard, T. (1977). An Alternative Approach to the Bradley-Terry Model for Paired Comparisons. Biometrics, 33, 121-132.
[16]
Aslam, M. (2002). Reference Prior For the Parameters of Rao-Kupper Model. Proc Pakistan Acad Sci., 39(2), 215-223.
[17]
Aslam, M. (2005). Bayesian Comparison of the Paired Comparison Models Allowing Ties. Journal of Statistical Theory and Applications, 4(2), 161-171.
[18]
Altaf, S., Aslam, M., & Aslam, M. (2012). Paired comparison analysis of the van Baaren model using Bayesian approach with noninformative prior. Pakistan Journal of Statistics and Operation Research, 8(2), 259-270.
[19]
Altaf, S., Aslam, M., & Aslam, M. (2013). Bayesian analysis of the van Baaren model for paired comparison. Hacettepe Journal of Mathematics and Statistics, 42(5), 569-80.
[20]
Satti, S., & Aslam, M. (2011). A Bayesian Look at the Pair Comparison Model with Tie and Order Effect. Proc. 8th International Conference on Recent Advances in Statistics, 223-234.
[21]
Bernardo, J. M. (1979). Reference Posterior Distribution for Bayesian Inference (with discussion). Journal of statistical planning and inference, 15, 265-278.
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