Eric Nyarko
In psychological research often paired comparisons are used in which either full or partial profiles of the alternatives described by a common set of two-level attributes are presented. For this situation the problem of finding optimal designs is considered in the presence of third-order interactions.
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It is shown how by not losing information on higher order interactions, optimal paired comparison designs involving alternatives of either full or partial profiles to reduce information overload as frequently encountered in applications can be constructed which enable identification of main effects up to third-order interactions when all attributes have general common number of levels.
For paired comparison experiments involving competing options described by two-level attributes several different methods of constructing designs having block paired observations under the main effects model are presented. These designs are compared to alternative designs available in the literature.
In paired comparison experiments respondents usually evaluate pairs of competing options. For this situation we introduce an appropriate model and derive optimal designs in the presence of second-order interactions when all attributes are dichotomous.
We present a Bayesian rating system based on the method of paired comparisons. Our system is a flexible generalization of the well-known Glicko, and in particular can better accommodate games with significant elements of luck. Our system is currently in use in the online game Duelyst II, and in that setting outperforms Glicko2.
A paired comparison analysis is the simplest way to make comparative judgments between objects where objects may be goods, services or skills. For a set of problems, this technique helps to choose the most important problem to solve first and/or provides the solution that will be the most effective. This paper presents the theory of paired comparisons method and contributes to the paired comparisons models by developing a new model based on t-distribution. The developed model is illustrated using a data set of citations among four famous journals of Statistics. Using Bayesian analysis, the jou…
In real life situations often paired comparisons involving alternatives of either full or partial profiles to mitigate cognitive burden are presented. For this situation the problem of finding optimal designs is considered in the presence of second-order interactions when all attributes have general common number of levels.
Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments have been proposed in different areas. This paper provides an updated overview of these extensions, including how to account for object- and subject-specific covariates and how to deal with ordinal paired comparison data. Special emphasis is given to models for dependent comparisons. Although these models are more realistic, their use is complicated by numerical difficulties. We therefore concentrate on implementation issues. In pa…
Semiparametric analysis for paired comparisons with covariates
本文提出半参数框架，通过引入未指定分布的潜在随机变量，解决高维配对比较数据中的模型不一致性问题，并推导了渐近正态分布。
Testing for lack of fit in paired comparison data
本文提出了一类检测 cardinal 成对比较模型中缺乏拟合性的检验方法，针对不同比较图增长规则设计了检验方法，提高了检验效能，并扩展到高维稀疏比较图。
Paired comparison models with strength-dependent ties and order effects
提出一种考虑平局和顺序效应且平局概率与顺序效应均随竞争者实力增强而增加的新型配对比较模型，并在国际象棋比赛数据上验证了其有效性。
Paired comparison models are used for analyzing data that involves pairwise comparisons among a set of objects. When the outcomes of the pairwise comparisons have no ties, the paired comparison models can be generalized as a class of binary response models. Receiver operating characteristic (ROC) curves and their corresponding areas under the curves are commonly used as performance metrics to evaluate the discriminating ability of binary response models. Despite their individual wide range of usage and their close connection to binary response models, ROC analysis to our knowledge has never be…
Inference in a generalized Bradley-Terry model for paired comparisons with covariates and a growing number of subjects
本研究提出含协变量的广义Bradley-Terry配对比较模型，证明了高维场景下最大似然估计的一致收敛性与渐近正态性，揭示了回归系数估计的渐近偏差现象，并将结果推广至Erdős–Rényi比较图，通过数值与真实数据验证了理论。
Modeling cyclicality and intransitivity in paired comparisons data
本文提出一种框架，用于建模循环性和非传递性，通过分解偏好轮廓为正交的传递和循环组件，明确循环性、非传递性和配对比较理论中几种传递性概念的关系，通过模拟和实证应用评估方法。
Brier-UDAM for Paired Prediction-Rule Comparisons: Latent-Risk Interpretation, Observable Contrasts, and Inference
提出Brier-UDAM框架，将配对预测规则的Brier风险差异分解为平均偏差、离散度和尺度对齐，实现潜在风险解释与推断，并在再入院分析中揭示隐藏抵消。
Regularization in Paired Comparison Models via Pseudo-Games and Phantom Players
针对成对比较模型中最大似然估计不稳定的问题，本文提出两种数据增广正则化方法：添加伪博弈和引入幻影玩家，产生有限收缩估计并解决位置不可识别性，在Bradley-Terry模型中与岭正则化效果相当。
This article introduces the bpcs R package (Bayesian Paired Comparison in Stan) and the statistical models implemented in the package. This package aims to facilitate the use of Bayesian models for paired comparison data in behavioral research. Bayesian analysis of paired comparison data allows parameter estimation even in conditions where the maximum likelihood does not exist, allows easy extension of paired comparison models, provide straightforward interpretation of the results with credible intervals, have better control of type I error, have more robust evidence towards the null hypothesi…
Tractable Ridge Regression for Paired Comparisons
针对成对比较模型的岭惩罚参数调节问题，提出结合经验贝叶斯与复合似然的免重拟合方法，模拟和英超28个赛季数据均表明其预测精度优于极大似然及标准偏差减少惩罚。
Comparison of predictive values with paired samples
针对配对样本下两种诊断测试的预测值比较，提出满足诊断与测试对称性的新推断方法，以简单表达式实现差值/比值的置信区间及单独与整体齐性检验，并选出最优方法。
In a wide class of paired comparisons, especially in the sports games, in which all subjects are divided into several groups, the intragroup comparisons are dense and the intergroup comparisons are sparse. Typical examples include the NFL regular season. Motivated by these situations, we propose group sparsity for paired comparisons and show the consistency and asymptotical normality of the maximum likelihood estimate in the Bradley-Terry model when the number of parameters goes to infinity in this paper. Simulations are carried out to illustrate the group sparsity and asymptotical results.
Least squares for cardinal paired comparisons data
本文严格分析基数成对比较数据图模型的最小二乘估计量，给出保证强相合性、渐近正态性和指数收敛的基于图的充要条件，并应用于NBA球队排名。
Generalized Bradley-Terry Models for Score Estimation from Paired Comparisons
本文提出广义Bradley-Terry（GBT）模型族，统一处理离散或连续成对比较，并证明其负对数似然严格凸、MAP估计存在唯一且对比较单调和Lipschitz弹性，兼具理论保证与实用价值。
Scientists often use a paired comparison of the areas under the receiver operating characteristic curves to decide which continuous cancer screening test has the best diagnostic accuracy. In the paired design, all participants are screened with both tests. Participants with unremarkable screening results enter a follow-up period. Participants with suspicious screening results and those who show evidence of disease during follow-up receive the gold standard test. The remaining participants are classified as non-cases, even though some may have occult disease. The standard analysis includes all …
A nonparametric relative treatment effect for direct comparisons of censored paired survival outcomes
针对右删失配对生存数据的治疗效果比较问题，提出基于竞争风险技术的非参数相对治疗效应估计方法，通过随机化重抽样实现推断，模拟显示功效优于传统方法，并在糖尿病视网膜病变数据集上验证了适用性。
Statistical Methods for Multiple Language Model Comparison on a Shared Evaluation
本文提出适用于共享评估的多语言模型比较统计方法，构建含模型固定效应、问题随机效应的随机效应模型，经模拟与真实数据验证，为多模型评估结果报告提供建议。
A General Framework for Design-Based Treatment Effect Estimation in Paired Cluster-Randomized Experiments
针对配对整群随机实验，提出一个基于设计的平均个体效应估计通用框架，阐明点估计的偏差-方差权衡，强调协变量调整的优势，并通过模拟研究比较不同估计量性能。
The authors give an approximation method for Bayesian inference in arena model, which is focused on paired comparisons with eliminations and bifurcations. The approximation method simplifies the inference by reducing parameters and introducing normal distribution functions into the computation of posterior distribution, which is largely based on an important property of normal random variables. Maximum a posteriori probability (MAP) and Bayesian prediction are then used to mine the information from the past pairwise comparison data, such as an individual's strength or volatility and his possib…
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