Article
Psychology, Mathematical
David Issa Mattos, Erika Martins Silva Ramos
Summary: The article introduces the bpcs R package and the statistical models it implements, aiming to facilitate the use of Bayesian models for paired comparison data in behavioral research. Bayesian analysis allows better control of type I error and provides stronger evidence towards the null hypothesis.
BEHAVIOR RESEARCH METHODS
(2022)
Article
Mathematics, Applied
Chao Gao, Yandi Shen, Anderson Y. Zhang
Summary: This paper focuses on the Bradley-Terry-Luce (BTL) model and its uncertainty quantification, specifically in the case of sparse comparison graphs. The maximum likelihood estimator (MLE) and spectral estimator are examined in this context, with the derivation of non-asymptotic expansions and the development of confident intervals and optimal constant of l(2) estimation as main contributions.
INFORMATION AND INFERENCE-A JOURNAL OF THE IMA
(2023)
Article
Chemistry, Physical
Aisha Fayomi, Rizwana Majeed, Ali Algarni, Sohail Akhtar, Farrukh Jamal, Jamal Abdul Nasir
Summary: Forecasting plays a crucial role in various fields, including decision-making in management, weather forecasting, and betting market activities such as tennis forecasting. The Bradley-Terry model is utilized to predict match outcomes in men's professional tennis matches, showing promising results compared to ATP rankings.
INTERNATIONAL JOURNAL OF PHOTOENERGY
(2022)
Article
Computer Science, Artificial Intelligence
Laszlo Gyarmati, Eva Orban-Mihalyko, Csaba Mihalyko, Zsombor Szadoczki, Sandor Bozoki
Summary: This paper investigates and compares pairwise comparison models and the stochastic Bradley-Terry model, and proves that they provide the same priority vectors for consistent comparisons. For incomplete comparisons, all filling in levels are considered. The simulations show that the optimal subsets and sequences for the Bradley-Terry model and the Thurstone model are also the same.
EXPERT SYSTEMS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Laszlo Gyarmati, Eva Orban-Mihalyko, Csaba Mihalyko
Summary: This paper investigates paired comparison models with stochastic background. We focus on models that allow three options for choice and estimate the parameters using the maximum likelihood method. The existence and uniqueness of the estimator are crucial in the evaluation. While a necessary and sufficient condition is given for two options by Ford in the Bradley-Terry model, we generalize this statement for the set of strictly log-concave distribution. In the case of three options, although the necessary and sufficient condition is unknown, we generalize and compare two different sufficient conditions. Computer simulations show that the new condition more frequently indicates the existence of the maximum compared to the previously known ones.
Article
Statistics & Probability
Pinhan Chen, Chao Gao, Anderson Y. Zhang
Summary: This paper considers the problem of ranking n players from partial pairwise comparison data under the Bradley-Terry-Luce model. For the first time, the minimax rate of this ranking problem is derived with respect to the Kendall's tau distance, which measures the difference between two rank vectors by counting the number of inversions. The minimax rate of ranking exhibits a transition between an exponential rate and a polynomial rate depending on the signal-to-noise ratio. To achieve the minimax rate, a divide-and-conquer ranking algorithm is proposed that first divides the players into groups and then computes local MLE within each group, and the optimality of the algorithm is established through an approximate independence argument.
ANNALS OF STATISTICS
(2022)
Article
Management
Yue Liu, Ethan X. Fang, Junwei Lu
Summary: We propose a novel combinatorial inference framework for uncertainty quantification in ranking problems. Our method considers the widely adopted Bradley-Terry-Luce (BTL) model and aims to infer general ranking properties, including local and global properties. We also extend the framework to multiple testing problems and derive an information-theoretic lower bound. Extensive numerical studies using synthetic and real datasets support our theory.
OPERATIONS RESEARCH
(2023)
Article
Social Sciences, Mathematical Methods
Weichen Wu, Nynke Niezink, Brian Junker
Summary: This paper proposes a framework for analyzing pairwise comparison data and develops diagnostics for both the objects being compared and the subjects making the comparisons. The proposed framework is illustrated using two survey data sets.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY
(2022)
Article
Management
Rose Baker, Philip Scarf
Summary: This paper introduces modified BT and PL models based on discrete distributions, primarily the geometric distribution, that can handle tied ranks, which are common in sports. The methodology is applied to various distributions, including some mathematically tractable ones, and illustrated using test match cricket data.
IMA JOURNAL OF MANAGEMENT MATHEMATICS
(2021)
Article
Statistics & Probability
Xin-Yu Tian, Jian Shi
Summary: This paper proposes a penalised spectral ranking method to simultaneously rank and group items with similar abilities. The method uses a fused lasso estimator in conjunction with a spectral-based method, rank centrality. Theoretical results and real examples are provided to demonstrate the effectiveness and practical significance of the proposed approach.
Article
Biochemical Research Methods
Ruping Sun, Athanasios N. Nikolakopoulos
Summary: This study utilizes mathematical and computational modeling to illuminate the fundamental elements and evolutionary determinants of metastatic-primary (M-P) genomic divergence, especially focusing on the impact of the primary tumor growth mode on the dependence of M-P divergence.
PLOS COMPUTATIONAL BIOLOGY
(2021)
Article
Computer Science, Software Engineering
Kaue de Sousa, David Brown, Jonathan Steinke, Jacob van Etten
Summary: Researchers in agricultural experiments require proper data management and analysis tools to gain insights from data. Programmatic tools are necessary to ensure reproducible workflows and routine applications. The R package gosset has been developed to address the need for rank-based data and models, providing functionality for data preparation, modeling, and result presentation. This paper demonstrates the package's features through a case study on decentralized on-farm trials of common bean varieties in Nicaragua.
Article
Statistics & Probability
Amadou Sawadogo, Simplice Dossou-Gbete
Summary: This paper focuses on the simulation of an extended Mallows-Bradley-Terry ranking probability model using the acceptance-rejection method. While a Monte Carlo Markov Chain (MCMC) algorithm has been proposed for large q values, the proposed tool emphasizes the importance of appropriate constant and instrumental distribution selection for generating samples from the target distribution, especially when the number of items to be ranked is small.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2022)
Article
Statistics & Probability
David J. Aldous, Brett Kolesnik
Summary: Larry Shepp's response to discovering that his work was not as original as he thought highlights the value he placed on his own discovery. In this article, the authors discuss and provide probabilistic proofs for two related but lesser-known results on random tournaments, which appear to be surprisingly unknown to modern probabilists. Their proof of Moon's theorem on mean score sequences is more constructive than previous proofs, providing a concrete introduction to the longstanding mystery of the lack of a canonical construction for a joint distribution in the representation theorem for convex order.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2022)
Article
Biology
Yan Li, Chun Yu, Yize Zhao, Weixin Yao, Robert H. Aseltine, Kun Chen
Summary: Researchers often face heterogeneous populations with mixed regression relationships in the era of data explosion. In such situations, identifying predictors associated with the outcome and distinguishing true sources of heterogeneity are of interest. A regularized finite mixture effects regression method is proposed for this purpose, achieving both heterogeneity pursuit and feature selection simultaneously with efficiency and consistency.
Article
Dentistry, Oral Surgery & Medicine
Florian Ortner, Marian Eberl, Sven Otto, Baocheng Wang, Gunther Schauberger, Klaus Hofmann-Kiefer, Thomas Saller
Summary: Dementia was found to be the only significant risk factor for postoperative delirium (POD) after general oral and maxillofacial surgery, with patients suffering from dementia at a higher risk of developing POD. Patients undergoing dentoalveolar surgery were typically younger, had higher anesthesiological risk, and were more likely to have other psychiatric and neurological disorders.
JOURNAL OF STOMATOLOGY ORAL AND MAXILLOFACIAL SURGERY
(2021)
Article
Statistics & Probability
Gerhard Tutz
Summary: Appropriate modelling of Likert-type items should consider the scale level and the specific role of the neutral middle category, and separate the neutral category to avoid biased estimates when modeling the effects of explanatory variables on the outcome. The proposed hierarchical model using binary response models as building blocks can be easily extended to include response style effects and non-linear smooth effects of explanatory variables.
INTERNATIONAL STATISTICAL REVIEW
(2021)
Article
Mathematics, Interdisciplinary Applications
Gerhard Tutz
JOURNAL OF MATHEMATICAL PSYCHOLOGY
(2020)
Article
Public, Environmental & Occupational Health
Sandra Bayer, Theresa Drabsch, Gunther Schauberger, Hans Hauner, Christina Holzapfel
Summary: The study revealed that the majority of participants were unfamiliar with the terms of personalised or genotype-based dietary recommendation, but a third of them showed interest in utilizing genotype-based dietary recommendations.
PUBLIC HEALTH NUTRITION
(2021)
Article
Statistics & Probability
Gunther Schauberger, Gerhard Tutz
Summary: Common random effects models for repeated measurements consider population heterogeneity with subject-specific intercepts or variable effects, but do not account for heterogeneity in answering tendencies. Extended models are proposed for ordinal responses, modeling location effects and tendencies based on explanatory variables. Ignoring response styles can impact parameter estimates, as shown in an example demonstrating the method's applicability.
STATISTICAL MODELLING
(2022)
Article
Engineering, Industrial
Maximilian J. Stanglmeier, Florian Schulte, Gunther Schauberger, Raphael J. Bichler, Ansgar Schwirtz, Florian K. Paternoster
Summary: This study investigated the space needed to cross legs while sitting in a vehicle, finding that movement execution is affected by legroom proportions, individual anthropometry, and flexibility. The use of predicted motion traces to determine spatial requirements of movements is also presented.
Article
Mathematics, Interdisciplinary Applications
Gerhard Tutz
Summary: The study introduces an improved method for ordinal trees that avoid the artificial assignment of scores and adopts the construction principle of binary models, combining trees and parametric models for prediction. The potential performance issues of random forests are also discussed, with proposals for ensemble models to achieve better predictive performance.
JOURNAL OF CLASSIFICATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Gerhard Tutz
Summary: A comprehensive class of models is proposed for various types of responses, including continuous, binary, ordered categorical, and count type responses. These models are flexible and can accommodate a wide range of distributions.
Article
Statistics & Probability
Ingrid Mauerer, Gerhard Tutz
Summary: This study proposes a flexible and general heterogeneous multinomial logit model to study differences in choice behavior. The model captures heterogeneity that classical models cannot capture, indicates the strength of heterogeneity, and allows for examining the explanatory variables causing heterogeneity.
STATISTICAL METHODS AND APPLICATIONS
(2023)
Article
Social Sciences, Mathematical Methods
Gerhard Tutz
Summary: A new item response theory model for count data is proposed, which does not assume a fixed distribution for the responses and shows good performance in recovering parameters and response distributions, as well as flexibility in accommodating varying response distributions.
APPLIED PSYCHOLOGICAL MEASUREMENT
(2022)
Article
Mathematical & Computational Biology
Gunther Schauberger, Luana Fiengo Tanaka, Moritz Berger
Summary: Conditional logistic regression (CLR) is the standard method for matched case-control studies, but it has limitations in including non-linear effects and interactions of confounding variables. A novel tree-based modeling method is proposed to address this issue and provide a flexible framework for a more complex confounding structure. The proposed machine learning model is fitted within the CLR framework, allowing for the consideration of matched strata. Simulation results demonstrate the effectiveness of the method, and it is applied to a cervical cancer case-control study for illustration.
STATISTICS IN MEDICINE
(2023)
Article
Education & Educational Research
Gerhard Tutz, Pascal Jordan
Summary: This article presents a general framework for latent trait item response models for continuous responses. Unlike classical test theory models, which differentiate between true scores and error scores, this model links the responses directly to latent traits. It is demonstrated that classical test theory models can be derived as special cases but the model class is much broader. The framework provides appropriate modeling for restricted responses, such as positive responses or responses within a certain interval. The model also extends common response time models and explores the role of the total score, leading to a modified total score. Various applications are illustrated, including one that considers covariates that may modify the response.
JOURNAL OF EDUCATIONAL AND BEHAVIORAL STATISTICS
(2023)
Review
Statistics & Probability
Gerhard Tutz
Summary: Ordinal models can be seen as being composed from simpler binary models, leading to a taxonomy of models; the structured overview covers existing models and shows how models can be extended to consider further effects of explanatory variables; particular attention is given to modeling additional heterogeneity and investigating the exact meaning of heterogeneity terms.
WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS
(2022)
Article
Oncology
Linda A. Liang, Thomas Einzmann, Arno Franzen, Katja Schwarzer, Gunther Schauberger, Dirk Schriefer, Kathrin Radde, Sylke R. Zeissig, Hans Ikenberg, Chris J. L. M. Meijer, Charles J. Kirkpatrick, Heinz Koelbl, Maria Blettner, Stefanie J. Klug
Summary: The study compared the strategies of stand-alone HPV testing and cotesting for cervical cancer screening in a population-based study in Germany. The results showed that cotesting had higher sensitivity but also resulted in more false positive results and colposcopy referrals compared to stand-alone HPV testing.
CANCER EPIDEMIOLOGY BIOMARKERS & PREVENTION
(2021)
Article
Hospitality, Leisure, Sport & Tourism
Andreas Groll, Jonas Heiner, Gunther Schauberger, Joern Uhrmeister
JOURNAL OF SPORTS ANALYTICS
(2020)
