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Journal articles on the topic 'Bradley Terry models'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Hunter, David R. "MM algorithms for generalized Bradley-Terry models." Annals of Statistics 32, no. 1 (2003): 384–406. http://dx.doi.org/10.1214/aos/1079120141.

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2

Caron, François, and Arnaud Doucet. "Efficient Bayesian Inference for Generalized Bradley–Terry Models." Journal of Computational and Graphical Statistics 21, no. 1 (2012): 174–96. http://dx.doi.org/10.1080/10618600.2012.638220.

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3

Tutz, Gerhard. "Bradley-Terry-Luce models with an ordered response." Journal of Mathematical Psychology 30, no. 3 (1986): 306–16. http://dx.doi.org/10.1016/0022-2496(86)90034-9.

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4

Casalicchio, Giuseppe, Gerhard Tutz, and Gunther Schauberger. "Subject-specific Bradley–Terry–Luce models with implicit variable selection." Statistical Modelling: An International Journal 15, no. 6 (2015): 526–47. http://dx.doi.org/10.1177/1471082x15571817.

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5

Fujimoto, Yu, Hideitsu Hino, and Noboru Murata. "An Estimation of Generalized Bradley-Terry Models Based on the em Algorithm." Neural Computation 23, no. 6 (2011): 1623–59. http://dx.doi.org/10.1162/neco_a_00129.

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The Bradley-Terry model is a statistical representation for one's preference or ranking data by using pairwise comparison results of items. For estimation of the model, several methods based on the sum of weighted Kullback-Leibler divergences have been proposed from various contexts. The purpose of this letter is to interpret an estimation mechanism of the Bradley-Terry model from the viewpoint of flatness, a fundamental notion used in information geometry. Based on this point of view, a new estimation method is proposed on a framework of the em algorithm. The proposed method is different in i

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6

Matthews, J. N. S., and K. P. Morris. "An Application of Bradley-Terry-Type Models to the Measurement of Pain." Applied Statistics 44, no. 2 (1995): 243. http://dx.doi.org/10.2307/2986348.

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7

Krese, Blaž, and Erik Štrumbelj. "A Bayesian approach to time-varying latent strengths in pairwise comparisons." PLOS ONE 16, no. 5 (2021): e0251945. http://dx.doi.org/10.1371/journal.pone.0251945.

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The famous Bradley-Terry model for pairwise comparisons is widely used for ranking objects and is often applied to sports data. In this paper we extend the Bradley-Terry model by allowing time-varying latent strengths of compared objects. The time component is modelled with barycentric rational interpolation and Gaussian processes. We also allow for the inclusion of additional information in the form of outcome probabilities. Our models are evaluated and compared on toy data set and real sports data from ATP tennis matches and NBA games. We demonstrated that using Gaussian processes is advanta

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8

Strobl, Carolin, Florian Wickelmaier, and Achim Zeileis. "Accounting for Individual Differences in Bradley-Terry Models by Means of Recursive Partitioning." Journal of Educational and Behavioral Statistics 36, no. 2 (2011): 135–53. http://dx.doi.org/10.3102/1076998609359791.

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9

Yan, Ting. "Ranking in the generalized Bradley–Terry models when the strong connection condition fails." Communications in Statistics - Theory and Methods 45, no. 2 (2016): 340–53. http://dx.doi.org/10.1080/03610926.2013.809114.

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10

Dittrich, R., W. Katzenbeisser, and H. Reisinger. "The analysis of rank ordered preference data based on Bradley-Terry Type Models." OR Spectrum 22, no. 1 (2000): 117–34. http://dx.doi.org/10.1007/s002910050008.

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11

Hankin, Robin,K ,S. "Partial Rank Data with the hyper2 Package: Likelihood Functions for Generalized Bradley-Terry Models." R Journal 9, no. 2 (2017): 429. http://dx.doi.org/10.32614/rj-2017-061.

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12

Augustin, Thomas. "Bradley - Terry - Luce models to incorporate within-pair order effects: Representation and uniqueness theorems." British Journal of Mathematical and Statistical Psychology 57, no. 2 (2004): 281–94. http://dx.doi.org/10.1348/0007110042307195.

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13

Jin, Tao, Pan Xu, Quanquan Gu, and Farzad Farnoud. "Rank Aggregation via Heterogeneous Thurstone Preference Models." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 4353–60. http://dx.doi.org/10.1609/aaai.v34i04.5860.

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We propose the Heterogeneous Thurstone Model (HTM) for aggregating ranked data, which can take the accuracy levels of different users into account. By allowing different noise distributions, the proposed HTM model maintains the generality of Thurstone's original framework, and as such, also extends the Bradley-Terry-Luce (BTL) model for pairwise comparisons to heterogeneous populations of users. Under this framework, we also propose a rank aggregation algorithm based on alternating gradient descent to estimate the underlying item scores and accuracy levels of different users simultaneously fro

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14

Batchelder, William H., Xiangen Hu, and Jared B. Smith. "Multinomial Processing Tree Models for Discrete Choice." Zeitschrift für Psychologie / Journal of Psychology 217, no. 3 (2009): 149–58. http://dx.doi.org/10.1027/0044-3409.217.3.149.

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This paper shows how to develop new multinomial processing tree (MPT) models for discrete choice, and in particular binary choice. First it reviews the history of discrete choice with special attention to Duncan Luce’s book Individual Choice Behavior. Luce’s choice axiom leads to the Bradley-Terry-Luce (BTL) paired-comparison model which is the basis of logit models of discrete choice used throughout the social and behavioral sciences. It is shown that a reparameterization of the BTL model is represented by choice probabilities generated from a finite state Markov chain, and this representatio

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15

Dras, Mark. "Evaluating Human Pairwise Preference Judgments." Computational Linguistics 41, no. 2 (2015): 337–45. http://dx.doi.org/10.1162/coli_a_00222.

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Human evaluation plays an important role in NLP, often in the form of preference judgments. Although there has been some use of classical non-parametric and bespoke approaches to evaluating these sorts of judgments, there is an entire body of work on this in the context of sensory discrimination testing and the human judgments that are central to it, backed by rigorous statistical theory and freely available software, that NLP can draw on. We investigate one approach, Log-Linear Bradley-Terry models, and apply it to sample NLP data.

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16

Ludden, Ian G., Arash Khatibi, Douglas M. King, and Sheldon H. Jacobson. "Models for generating NCAA men’s basketball tournament bracket pools." Journal of Quantitative Analysis in Sports 16, no. 1 (2020): 1–15. http://dx.doi.org/10.1515/jqas-2019-0022.

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AbstractEach year, the NCAA Division I Men’s Basketball Tournament attracts popular attention, including bracket challenges where fans seek to pick the winners of the tournament’s games. However, the quantity and unpredictable nature of games suggest a single bracket will likely select some winning teams incorrectly even if created with insightful and sophisticated methods. Hence, rather than focusing on creating a single bracket to perform well, a challenge participant may wish to create a pool of brackets that likely contains at least one high-scoring bracket. This paper proposes a power mod

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17

Ley, Christophe, Tom Van de Wiele, and Hans Van Eetvelde. "Ranking soccer teams on the basis of their current strength: A comparison of maximum likelihood approaches." Statistical Modelling 19, no. 1 (2019): 55–73. http://dx.doi.org/10.1177/1471082x18817650.

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We present 10 different strength-based statistical models that we use to model soccer match outcomes with the aim of producing a new ranking. The models are of four main types: Thurstone–Mosteller, Bradley–Terry, independent Poisson and bivariate Poisson, and their common aspect is that the parameters are estimated via weighted maximum likelihood, the weights being a match importance factor and a time depreciation factor giving less weight to matches that are played a long time ago. Since our goal is to build a ranking reflecting the teams’ current strengths, we compare the 10 models on the ba

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18

Augustin, Thomas. "An approach to combine the logistic threshold model of psychophysics with the Bradley–Terry–Luce models of choice theory." Journal of Mathematical Psychology 49, no. 1 (2005): 70–79. http://dx.doi.org/10.1016/j.jmp.2004.11.002.

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19

Shev, Aaron, Fushing Hsieh, Brianne Beisner, and Brenda McCowan. "Using Markov chain Monte Carlo (MCMC) to visualize and test the linearity assumption of the Bradley–Terry class of models." Animal Behaviour 84, no. 6 (2012): 1523–31. http://dx.doi.org/10.1016/j.anbehav.2012.09.026.

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20

CHEN, SHUMING, DENGFENG WANG, and JIE LIANG. "SOUND QUALITY ANALYSIS AND PREDICTION OF VEHICLE INTERIOR NOISE BASED ON GREY SYSTEM THEORY." Fluctuation and Noise Letters 11, no. 02 (2012): 1250016. http://dx.doi.org/10.1142/s0219477512500162.

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This paper presents a novel effective methodology for sound quality analysis and prediction of vehicle interior noise using gray system theory. Four objective psychoacoustic parameters selected to evaluate acoustic performance of vehicle interior environment are loudness, sharpness, roughness, and fluctuation. Subjective evaluation is presented using paired comparison method, and Bradley–Terry model is also created. The relationship between subjective evaluation and psychoacoustic parameters is determined by using gray relational analysis. Meanwhile, the correlation among psychoacoustic parame

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21

Liu, Qinghua, Marta Crispino, Ida Scheel, Valeria Vitelli, and Arnoldo Frigessi. "Model-Based Learning from Preference Data." Annual Review of Statistics and Its Application 6, no. 1 (2019): 329–54. http://dx.doi.org/10.1146/annurev-statistics-031017-100213.

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Preference data occur when assessors express comparative opinions about a set of items, by rating, ranking, pair comparing, liking, or clicking. The purpose of preference learning is to ( a) infer on the shared consensus preference of a group of users, sometimes called rank aggregation, or ( b) estimate for each user her individual ranking of the items, when the user indicates only incomplete preferences; the latter is an important part of recommender systems. We provide an overview of probabilistic approaches to preference learning, including the Mallows, Plackett–Luce, and Bradley–Terry mode

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22

Aktaş, Serpil, Melike Bahçecitapar, and Rıfat Ergan. "Bradley-Terry Modeli ile Türkiye Basketbol Süper Ligi’nde Takımların Ev Sahibi Olma Avantajının İncelenmesi." Spor Bilimleri Dergisi Hacettepe Üniversitesi 29, no. 1 (2018): 15–26. http://dx.doi.org/10.17644/sbd.335508.

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23

Firth, David. "Bradley-Terry Models inR." Journal of Statistical Software 12, no. 1 (2005). http://dx.doi.org/10.18637/jss.v012.i01.

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24

Turner, Heather, and David Firth. "Bradley-Terry Models inR: TheBradleyTerry2Package." Journal of Statistical Software 48, no. 9 (2012). http://dx.doi.org/10.18637/jss.v048.i09.

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25

Singh, Akshay Kumar, and Shubhabratha Das. "Rank Consistent Bradley-Terry Models for Repeated Tournaments." SSRN Electronic Journal, 2014. http://dx.doi.org/10.2139/ssrn.2464964.

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26

Dewart, Neil, and Jonathan Gillard. "Using Bradley–Terry models to analyse test match cricket." IMA Journal of Management Mathematics, January 8, 2018. http://dx.doi.org/10.1093/imaman/dpx013.

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27

Baker, Rose, and Philip Scarf. "Modifying Bradley–Terry and other ranking models to allow ties." IMA Journal of Management Mathematics, December 9, 2020. http://dx.doi.org/10.1093/imaman/dpaa027.

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Abstract Models derived from distributions of order-statistics are useful for modelling ranked data. The well-known Bradley–Terry (BT) and Plackett–Luce (PL) models can be derived from the order statistics of the exponential distribution but cannot handle ties. However, ties often occur in sports, and the ability to accommodate them leads to more useful ranking models. In this paper, we use discrete distributions, principally the geometric distribution, to obtain modified BT and PL models and some others that allow tied ranks. Our methodology is introduced for some mathematically tractable and

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28

Balreira, E. Cabral, and Brian K. Miceli. "Improving Foresight Predictions in the 2002-2018 NFL Regular-Seasons: A Classic Tale of Quantity vs. Quality." Journal of Advances in Mathematics and Computer Science, October 25, 2019, 1–14. http://dx.doi.org/10.9734/jamcs/2019/v34i1-230203.

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Utilizing a modied Bradley-Terry model, we develop a method of making foresight predictions of 2002-2018 NFL games by incorporating a home-eld parameter into previously established ranking models. Knowing only the home team and score of each contest, and taking into account previous predictions, we optimize this parameter considering one of two things: the quantity of correct picks to date or the quality of predictions to date as measured by a quadratic scoringfunction. Our main results establish that optimization of quality-rather than quantity-when making a prediction has higher overall accu

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29

Swanson, Nathan, Donald Koban, and Patrick Brundage. "Predicting the NHL playoffs with PageRank." Journal of Quantitative Analysis in Sports 13, no. 4 (2017). http://dx.doi.org/10.1515/jqas-2017-0005.

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AbstractApplying Google’s PageRank model to sports is a popular concept in contemporary sports ranking. However, there is limited evidence that rankings generated with PageRank models do well at predicting the winners of playoffs series. In this paper, we use a PageRank model to predict the outcomes of the 2008–2016 NHL playoffs. Unlike previous studies that use a uniform personalization vector, we incorporate Corsi statistics into a personalization vector, use a nine-fold cross validation to identify tuning parameters, and evaluate the prediction accuracy of the tuned model. We found our rati

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30

Schauberger, Gunther, and Gerhard Tutz. "BTLLasso: A Common Framework and Software Package for the Inclusion and Selection of Covariates in Bradley-Terry Models." Journal of Statistical Software 88, no. 9 (2019). http://dx.doi.org/10.18637/jss.v088.i09.

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