Welcome to Open Science
Contact Us
Home Books Journals Submission Open Science Join Us News
Paired Comparison Model: A Bayesian Non-Informative Analysis
Current Issue
Volume 3, 2015
Issue 4 (August)
Pages: 29-32   |   Vol. 3, No. 4, August 2015   |   Follow on         
Paper in PDF Downloads: 64   Since Oct. 10, 2015 Views: 1633   Since Oct. 10, 2015
Authors
[1]
Sadia Qamar, Department of Statistics, University of Sargodha, Sargodha, Pakistan.
[2]
Amna Nazeer, School of Mathematics and Statistics, Hua Zhong University of Science and Technology, Wuhan, China.
[3]
Samina Satti, Department of Statistics, University of Wah, Wah Cantt, Pakistan.
Abstract
Application of Bayesian inferential methods has become very appealing to almost every area of research. The current study also focuses on the Bayesian analysis of the van Baaren model-IV for paired comparisons. Use of prior information in form of probability distribution to update the available information is the key step of Bayesian analysis. We have considered the non-informative uniform prior for the analysis of the paired comparison model. Along with the treatment parameters the model also contains threshold or tie parameter and with-in pair order effect parameter. The joint posterior distribution is derived and evaluated to obtain the posterior means, posterior modes and posterior standard deviations. To deal with the estimation of multiparameters the Gibbs sampling scheme was used. The results supported the presence of the with-in pair order effect and the treatment presented first in the comparison of the pair had an advantage of being preferred. The preference and posterior probabilities also validated the findings of the posterior estimates.
Keywords
Paired Comparison Model, Bayesian Inference, Uniform Prior
Reference
[1]
David, H. A., (1988). The Method of Paired Comparisons. 2nd Eds. London: Griffin.
[2]
Bradley, R. A., & Terry, M. E. (1952). Rank analysis of Incomplete Block Designs, I. The method of Paired Comparisons. Biometrika, 39, 324-345.
[3]
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.
[4]
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.
[5]
Davidson, R. R., & Beaver, R. J. (1977). On Extending the Bradley-Terry Model to Incorporate Within Pair Order Effects. Biometrics, 33, 693-702.
[6]
Baaren, A. V. (1978). On a Class of Extension to the Bradley-terry Model in Paired Comparisons. Statistica Neerlandica, 32, 57-67.
[7]
Trawinski, B. J. (1965). An Exact Probability Distribution over Sample Spaces of Paired Comparisons. Biometrics, 21, 986-1000.
[8]
Singh, J. (1976). A Note on Pair Comparison Rankings. The Annals of Statistics, 4(3), 651-654.
[9]
Davidson, R. R., & Farquhar, P. H. (1976). A bibliography on the method of paired comparisons. Biometric, 32, 241–252.
[10]
Smith, A. F., & Gelfand, A. E. (1992). Bayesian statistics without tears: a sampling–resampling perspective. The American Statistician, 46(2), 84-88.
[11]
Gelfand, A. E., Smith, A. F., & Lee, T. M. (1992). Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. Journal of the American Statistical Association, 87(418), 523-532.
[12]
Davidson, R. R., & Solomon, D. L. (1973). A Bayesian Approach to Paired Comparison Experiments. Biometrika, 60(3), 477-487.
[13]
Leonard, T. (1977). An Alternative Approach to the Bradley-Terry Model for Paired Comparisons. Biometrics, 33, 121-132.
[14]
Aslam, M. (2002). Reference Prior For the Parameters of Rao-Kupper Model. Proc Pakistan Acad Sci., 39(2), 215-223.
[15]
Aslam, M. (2005). Bayesian Comparison of the Paired Comparison Models Allowing Ties. Journal of Statistical Theory and Applications, 4(2), 161-171.
[16]
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.
[17]
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.
[18]
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.
Open Science Scholarly Journals
Open Science is a peer-reviewed platform, the journals of which cover a wide range of academic disciplines and serve the world's research and scholarly communities. Upon acceptance, Open Science Journals will be immediately and permanently free for everyone to read and download.
CONTACT US
Office Address:
228 Park Ave., S#45956, New York, NY 10003
Phone: +(001)(347)535 0661
E-mail:
LET'S GET IN TOUCH
Name
E-mail
Subject
Message
SEND MASSAGE
Copyright © 2013-, Open Science Publishers - All Rights Reserved