STATISTICAL ANALYSIS OF THE TM- MODEL VIA BAYESIAN APPROACH

Abstract

The method of paired comparisons calls for the comparison of treatments presented in pairs to judges who prefer the better one based on their sensory evaluations. Thurstone (1927) and Mosteller (1951) employ the method of maximum likelihood to estimate the parameters of the Thurstone-Mosteller model for the paired comparisons. A Bayesian analysis of the said model using the non-informative reference (Jeffreys) prior is presented in this study. The posterior estimates (means and joint modes) of the parameters and the posterior probabilities comparing the two parameters are obtained for the analysis. The predictive probabilities that one treatment (Ti) in preferred to any other treatment (Tj) in a future single comparison are also computed. In addition, the graphs of the marginal posterior distributions of the individual parameter are drawn. The appropriateness of the model is also tested using the Chi-Square test statistic.