The use of limit theorems in paired comparison model building

Psychometrika ◽  
1967 ◽  
Vol 32 (3) ◽  
pp. 255-264 ◽  
Author(s):  
W. A. Thompson ◽  
Jagbir Singh
Keyword(s):  
Limit Theorems ◽  
Model Building ◽  
Paired Comparison ◽  
Comparison Model

Remarks about a paired comparison model

Psychometrika ◽  
1960 ◽  
Vol 25 (4) ◽  
pp. 357-367 ◽  
Author(s):  
Gottfried E. Noether
Keyword(s):  
Paired Comparison ◽  
Comparison Model

scholarly journals Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Khalil Ullah ◽  
Muhammad Aslam
Keyword(s):  
Loss Function ◽  
Goodness Of Fit ◽  
Numerical Approximation ◽  
Paired Comparison ◽  
Estimation Procedure ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Chi Square ◽  
Squared Error Loss Function ◽  
Comparison Model

The method of paired comparisons (PC) is widely used to rank items using sensory evaluations. The PC models are developed to provide basis for such comparisons. In this study, the Weibull PC model is analyzed under the Bayesian paradigm using noninformative priors and different loss functions, namely, Squared Error Loss Function (SELF), Quadratic Loss Function (QLF), DeGroot Loss Function (DLF), and Precautionary Loss Function (PLF). Numerical approximation is used to illustrate the entire estimation procedure. A real dataset showing usage preferences for different cellphone brands, Huawei (HW), Samsung (SS), Oppo (OP), QMobile (QM), and Nokia (NK), is used. Quadrature method is used to evaluate the Bayes estimates, their posterior risks, preference probabilities, predictive probabilities, and posterior probabilities to establish and verify ranking order of the competing cellphone brands under study. The results show that the paired comparison model under the study using Bayesian approach involving various loss functions can offer mathematical approach to evaluate cellphone brand preferences. The ranking provided by the model is justifiable according to the usage preference for these cellphone brands. The ranking given by the model indicates that cellphone brand Samsung is preferred the most and QMobile is the least preferred. The plausibility of the model is also assessed using the Chi square test of goodness of fit.

scholarly journals Estimation of final standings in football competitions with a premature ending: the case of COVID-19

2021 ◽  
Author(s):  
P. Gorgi ◽  
S. J. Koopman ◽  
R. Lit
Keyword(s):  
Historical Data ◽  
Paired Comparison ◽  
Performance Measure ◽  
League Table ◽  
Empirical Results ◽  
Comparison Model ◽  
Model Based ◽  
Alternative Approach

AbstractWe study an alternative approach to determine the final league table in football competitions with a premature ending. For several countries, a premature ending of the 2019/2020 football season has occurred due to the COVID-19 pandemic. We propose a model-based method as a possible alternative to the use of the incomplete standings to determine the final table. This method measures the performance of the teams in the matches of the season that have been played and predicts the remaining non-played matches through a paired-comparison model. The main advantage of the method compared to the incomplete standings is that it takes account of the bias in the performance measure due to the schedule of the matches in a season. Therefore, the resulting ranking of the teams based on our proposed method can be regarded as more fair in this respect. A forecasting study based on historical data of seven of the main European competitions is used to validate the method. The empirical results suggest that the model-based approach produces more accurate predictions of the true final standings than those based on the incomplete standings.

Optimal design for the Bradley–Terry paired comparison model

2007 ◽  
Vol 17 (3) ◽  
pp. 275-289 ◽  
Author(s):  
Ulrike Graßhoff ◽  
Rainer Schwabe
Keyword(s):  
Optimal Design ◽  
Paired Comparison ◽  
Comparison Model
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